#appropriate semicolon use

[correctopinionhaver]

there's no such thing as a midwife. no wife is mid; they're all exceptionally beautiful queens.

[caruliaa]

btw being annoying abt this thing that happened almost a week ago at this point bc had no tumblr then but i remember at one point when we were with our cousins and kinda just chatting and hanging out nd stuff my sibling just like. was repeatedly like being mean and insulting me for the most minor things and like it was rude but didnt rly hurt that much it was j whatever yk but they kept doing this but i was mostly like whatever even though they were being pretty mean nd at some point they were like "go walk of a cliff" and i was jokingly like "ill tell mum you said that" and then they were like "well you can tell that to her but i can tell her things too yk" basically threatening to out me or like. tell our parents about me having online friends and shit which is a pretty fucked thing to say and like. a completely inordinate reaction to me making a joke but we were around other ppl nd my i wasnt out to one of the cousins so i cldnt be like "hey what the fuck is wrong with you for threatening to out me over a joke" so i was just like "you kept insulting me and our cousins thats rude!" and then they got so sulky and was like "oh im not allowed to insult people but people are allowed to insult me?" even though that like. i never said that ?? and none of us were insulting them ??? and when i was like "i never said that its wrong for people to insult you too" they started talking about how im allowed to be annoying though and thats not fair when they cant insult me or whatever. hi.

[perpetual-stories]

Common Grammar Mistakes: Part 1

Hello, hello. It’s me coming back at ya with another segment of grammar basics. Last time I posted about grammar, I had talked about punctuation. This time I will be going over common grammar mistakes that writers often make. Plus it’s been a while since I’ve posted about grammar.

1. Run-on Sentences and Comma Splices

Run-on sentences are known to be sentences that combine independent clauses without punctuation or the right conjunction needed.

Comma splices are known to be similar to run-on sentences but instead uses commas to combine two clauses that have no appropriate conjunction.

I know, I sometimes fall victim to comma splices.

Fixing a run-on sentence or a comma splice can be done in five methods.

Sentence example: Rachel is very smart, she began reading when she was three years old.

Solution 1: Separate the clauses into two sentences: Rachel is very smart. She began reading when she was three years old.

Solution 2: Replace the comma with a semicolon (my favorite one): Rachel is very smart; she began reading when she was three years old.

Solution 3: Replace the comma with a coordinating conjunction: “Rachel is very smart, for she began reading when she was three years old.”

Solution 4: Replace the comma with a subordinating conjunction. “Rachel is very smart because she began reading when she was three years old.”

Solution 5: Replace the comma with a semicolon and transitional word or phrase. “Rachel is very smart; as a result, she began reading when she was three years old.”

Pronoun Disagreement

Some of the most common grammar mistakes are pronoun errors. They occur when pronouns do not agree in number with the nouns to which they refer. If the noun is singular, the pronoun must be singular. If the noun is plural, the pronoun must be plural as well. For example:

Incorrect: “Every girl must bring their own lunch.

Correct: “Every girl must bring her own lunch.”

Pronoun errors are common in modern English, as writers try to avoid awkward phrasing or the implication of sexist language. Although this is an admirable goal, it is still important to learn the correct grammar and use it in more formal situations.

Mistakes in Apostrophe Usage

Apostrophes are used to show possession. However, you do not use an apostrophe after a possessive pronoun such as my, mine, our, ours, his, hers, its, their, or theirs. For example:

Incorrect: “My mothers cabin is next to his' cabin.”

Correct: “My mother's cabin is next to his cabin.”

In the case of it's, the apostrophe is used only to indicate a contraction for “it is.” For example:

Incorrect: “Its a cold day for October.”

Correct: “It's a cold day for October.”

Lack of Subject-Verb Agreement

Confusion over subject-verb agreement can be the source of many grammatical errors. When speaking or writing in the present tense, a sentence must have subjects and verbs that agree in number. If the subject is singular, the verb must be singular. If the subject is plural, the verb must be plural as well. For example:

Incorrect: “These recipes is good for beginning chefs.”

Correct: “These recipes are good for beginning chefs.”

Misplaced Modifiers

To clearly communicate your ideas, you should place a modifier directly next to the word it is supposed to modify. The modifier should clearly refer to a specific word in the sentence. Misplaced modifiers can create confusion and ambiguity. For example:

Incorrect: “At eight years old, my father gave me a pony for Christmas.”

Correct: “When I was eight years old, my father gave me a pony for Christmas.”

Sentence Fragments

Sentence fragments are also common grammar mistakes. A sentence needs to have a subject and a verb. A fragment often happens after another related idea has been expressed. For example:

Incorrect: “Sharon stayed home from school the other day. Because she was sick.”

Correct: “Sharon stayed home from school the other day because she was sick.”

Missing Comma in a Compound Sentence

A compound sentence expresses two complete and related ideas, and it usually includes a conjunction to connect these two parts. There should be a comma before the conjunction to indicate the two ideas are related. If that’s missing, it’s a mistake readers will notice. For example:

Incorrect: “Jim went to the store and Ella went with him.”

Correct: “Jim went to the store, and Ella went with him.”

No Clear Antecedent

An antecedent is a word that comes before a pronoun and helps the reader understand what the pronoun means. Generally, you can clear up this confusion by rearranging the wording. For example:

Incorrect: “The dad found the boy, and he was happy.”

Correct: “The dad was happy when he found the boy.”

Ending a Sentence in a Preposition

Another common grammar mistake is ending a sentence with a preposition. A preposition, by its nature, indicates that another word will follow it. In casual conversation, this type of error is no big deal, but you should avoid this mistake in your writing. For example:

Incorrect: “What reason did he come here for?”

Correct: “For what reason did he come here?”

Please follow, like, comment and reblog!

[ivy-diaries]

⋮  — ⧉ . . viewing her body modifications:

ᝰ her tattoos:

i. the angel wings are a tribute to all the loved ones she lost, which includes a lot of her idol and real friends.

ii. the tattoo is a reference to jonghyun, who ivy admired and loved very much. It translates to "you did well. You worked really hard. Goodbye"

iii. Ivy got the inspiration for this tattoo from her lovely grandmother who actually had this tattoo and explained the meaning to her which is, " a semicolon is used when an author could've ended the sentence but chose not to. The author is you and the sentence is your life"

iv. ivy has a habit of getting random tattoos that fit her aesthetic and one out of the nine tattoos that she has, a few of them including this one that says "joy" is indeed random.

v. she had gotten this tattoo "angel" as it is one of many nicknames her boyfriend calls her and since he's very special to her, she decided to get his way of calling her inked.

vi. as many may already know, ivy's a pisces and so it was just appropriate that she'd get a symbol of her sign inked.

vii. the tattoo "½" is the one that she shares with her twin sister. Since the kang sisters don't see eachother quite often, their bond is shared by this tattoo.

viii. this one yet again a random flower that looked nice in the tattoo salon.

xi. this tattoo that says "love always" holds a very special place in the kang family because it is a tattoo that the twins and their mother share. The meaning is quite significant as these were the words ivy's grandmother used to repeat a lot and is the last word she ever said to them before she passed away.

ᝰ her piercings:

i. she has a total of seven piercings, four on her right ear and three on her left

[max1461]

Computer language that I want to use:

Everything is just a function, some of which output types. The semicolon is just a composition operator that outputs something with the appropriate (co?)product type, or whatever. I don't know the details but it should work. Indentation and line breaks are ignored.

You can hate me if you want.

[bmpmp3]

everyone always talks about people overusing semicolons and/or wanting to use them in incorrect places but i have like the opposite situation. im like desperately escaping semicolons at every turn. im a colon freak and im a big fan of dashes and commas, and of course the classic and wonderful parenthetical asides. but having to use a semicolon because its the most appropriate punctuation for a sentence makes me feel like ive been defeated. it feels like ive lost a war i didnt know i was fighting in. against semicolons. maybe i took people complaining about semicolon overuse as a challenge like ten years ago and forgot?

[frodo-with-glasses]

4, 6, 13 (especially 13; love you for the semicolon tattoo Frodo has)

https://www.tumblr.com/frodo-with-glasses/711440150764355584/group-chat-shenanigans?source=share

Ooh, great choice >:-D Let’s go!

(Read the whole comic here!)

4. What part of this piece was the most difficult to draw?

It's exactly what you might expect: Frodo's left arm (the one holding the phone) in the last panel definitely gave me some trouble. I was trying to find a pose that both a) looked natural and b) made Frodo's tattoo visible; you can actually see how many lines I drew and erased in the zoomed-in picture in this reblog.

I also had to try multiple different positions and designs for the tattoo before I found one that I liked. In a few early attempts, the tattoo actually went down the length of his arm! But in the end, I'm glad I kept it contained to the wrist.

6. What is your favorite part of this piece?

Oh man, it's so hard to pick! I love all of the modern designs, and I think most of the drawings turned out really well. (Pippin looks a bit wonky, but that's just because I'm not used to drawing people who are upside down.) In the end, I think my favorite part is just the slew of "Benadryl Cabbagepatch" names. That was a HYSTERICAL day on the Fig Tree Server, and I love seeing everyone's creativity and crazy senses of humor coming together like this! X-D

13. What Easter eggs/small details are hidden in this drawing?

OKAY *cracks knuckles* lemme give you the whole breakdown here.

Usernames and Avatar Icons

Frodo - DownFromTheDoor (referencing Bilbo's poem) - a book (because he's a nerd)

Pippin - tookursnacks (because he's a Took and he likes to eat) - peace sign (dunno, just felt appropriate)

Sam - taterz (obvious) - a potato (also obvious)

Merry - Herbmaster (because he really likes pipeweed) - the Horn of Rohan

Fatty - BigPapa (because he's. he's big) - plus signs (see previous)

Rosie - RoseGardens (cute play on her name) - a rose (same)

Gimli - Rock-n-Roll (dwarves like rocks) - an axe (obvious)

Aragorn - Telcontar (Elvish for "Strider", the dynasty name Aragorn chooses for himself) - crown surrounded by seven stars (part of the sigil of the King of Gondor)

Legolas - TraLaLally (reference to the 1977 Hobbit movie) - bow and arrow (obvious)

Boromir - TEAMGONDOR (in all caps because he is A LotTM) - the Horn of Gondor (obvious)

Tom Bombadil - Tim Bimbadimdim (I thought it would be funny) - a feather (he has one in the brim of his hat)

Goldberry - 💛🫐 (suggested by someone on the server, unfortunately not at all obvious in a black-and-white art style) - a star (seemed appropriate)

Gandalf - Gandalf (obvious) - wizard's hat (also obvious)

Design Choices

All four of the main hobbits (Frodo, Sam, Merry, Pippin) have a bracelet with a Single Bead, indicating they are part of the Core Friend Group

Merry wears dog tags and a watch. I imagine he has served in the military in some capacity, or aspires to do so; and the watch is there because he's the kind of detail-oriented person who's very concerned with being on time.

Sam and Rosie have matching bracelets: his is the sun, and hers is the moon. (Someone pointed out that the little thing hanging off her phone also looks like a sun. This is correct, but the bracelets were supposed to be the matching set.)

Rosie is also the only one of the gang to have a decorative phone case and a PopSocket.

Aragorn's mug says "GONDOR U", and the icon on his laptop is the shards of Narsil. It's kinda hard to see, but he also has a ring on his left hand, indicating that he's either engaged or married to Arwen.

Frodo gets the most Easter eggs. He too has a watch, because he's the sort to at least TRY to be on time; he has the tattoo, reading "worth f;ghting for", as aforementioned; and his shirt is a polo from the company Hang Ten, as indicated by the little feet embroidered on the lapel! I chose that one for two reasons: number one, little feet is Very Hobbity, and number two, they're my dad's favorite brand of polo. (He likes the little feet.)

PHONE DETAILS. Merry, Pippin, and Legolas are the only ones to have Extremely Fancy New Phones with three cameras on the back, because they are rich kids who can afford to have that sort of thing. Gimli is also rich, but his phone only has two cameras because he's not an Instagrammer. Sam and Rosie only have two-camera phones because theirs are cheaper older models. Everyone has phone cases except for Legolas. Gimli's phone case is a Particularly Chunky Heavy-Duty OtterBox. Aragorn is the only one with a laptop because he's Old. And, as aforementioned, Rosie is the only one who has a PopSocket.

Initial Conversation

I did actually plan the chat in the first panel very carefully! If you look at the time stamps beside the messages, you can see how the conversation picks up speed. It starts with Frodo declining some kind of an activity that night, saying he's busy with something else. Pippin responds, asking what he's doing. Frodo replies and sends photographic evidence, calling Bilbo "Beebo". Sam thinks this is very funny and repeats "Beebo". Frodo, encouraged by Sam thinking this is funny, doubles down the joke with "Beebo Bongos". Then Merry jumps in with "Blorbo Bagpipes". By this point, messages are coming in within the same minute, and then the rest of the chaos unfolds. X-D

Anyway, thanks for giving me an excuse to ramble about this comic! I had a lot of fun drawing it and I'm delighted to share the Deep Lore LOL

ARTIST COMMENTARY ASK GAME!

[accessibleaesthetics]

Hello! First of all I love your blog. I hope it's alright to ask you, as I don't know who else to turn to for this:

Do you think typical tone tags (with the slash and not spelled fully) are accessible to people with screen readers? Is the audio output generally harder to decipher than shortened tone tags are to visually read?

I haven't had to use them on my blog yet, but I might need to specify the tone at some point if it's ever particularly unclear. Do you have any tips on trying to reconcile accessibility for everyone?

Also… I sometimes use old-style emoticons, it's a typing style I find difficult to let go of, but I always write what it's supposed to represent in square brackets afterwards cause I know screen readers would just output "semicolon, closed parenthesis" and make zero sense to anyone. Do you think this method is more, less, or equally as accessible as just using a winking emoji (which would output "winking face emoji" I'm guessing)? I know using neither would be the top choice, but sometimes it feels appropriate to include a facial expression. Thanks for your time.

Thank you so much!

I'd say tone tags probably aren't the most accessible since they're going to be read out as phonetically as possible (also, many screen readers won't read the "slash"). There are also accessibility issues with them outside of that in the sense that not everyone knows what they mean, and that can create more confusion than clarity sometimes. If I have to stare at "could you please tag this next time? /nm" for a solid minute trying to figure out why someone asked me to tag something and then immediately told me "never mind," it's not the most efficient tool.

But at the end of the day, tone indicators are also an accessibility tool themselves. And they really help some people! So you could always try a happy medium with "could you please tag this next time? (not mad)" instead. That will generally convey your message more clearly to most people, screen reader user or not.

As for old style emoticons, that's a bit tricky. There are some screen readers, like VoiceOver, that will read :) as "smiley." Others, like JAWS, will read it either as "colon right paren" or just not read it at all, depending on what you have the verbosity settings at. But once you get more complicated than a smiley face or maybe a frowny face, you're getting a literal reading a best. Every screen reader I've tried can read all emojis just fine, but I'm told that's not universal either, so some people like to do a plain text version after, like this 👍 (thumbs up emoji).

Also fun fact, with VoiceOver at least, it doesn't read 😉 as "winking face emoji," it's just "winking face."

So all that said, I'm personally a big fan of emojis, especially as tone indicators, because they save me and my friends so much stress when talking to each other (for example "alright" could mean they're mad, but if you add a smiley after it, there is no way to overthink it.)

[angorwhosebabyisthis]

Useful tool for journaling games when you're having trouble figuring out what to write for a scene, even with the help of tables and other prompts: choose and/or roll for a certain number of sentences. Whatever the events of the entry/turn you're rolling for, they'll need to fill up that number of sentences.

You can write them out in whatever format you want--as a summary, prose description, or alternating between them.

You can write a more fleshed-out version of the events you decide on if you want, as long as it can be summarized by the target number of sentences.

You can limit yourself to that specific number of sentences if you want the extra bit of challenge, or keep going if you feel like it once you've met the target.

You don't have to write the prompt sentences before you write out, or roll for, an extended version of the scene if you decide to do that. You can start with the opening situation and then add summarizing sentences for events as they play out, or you can summarize after the scene is finished.

You can choose different ranges if you want (recommended if you find yourself stumped a lot as to length you want to go for), or just use the same one every time. You might, say, choose or roll between a 5-sentence entry, a 10-sentence entry, a 20-sentence entry, and so on, or you might just treat each prompt as requiring 5 sentences. You can implement this as a table, or by rolling the appropriate die for the range you want to aim for.

You can choose set numbers for each range if you want to use more than one, or you can roll within a certain range. 1-sentence prompts might be an entirely separate result from 3-sentence prompts and 5-sentence prompts, or you might roll 1-5 when you get the associated range. (Or 3-5, for that matter.)

You can designate specific ranges to different circumstances. A 20-sentence description might be appropriate for, say, establishing a new location for the first time, but chances are good you're going to want to mostly stick to 1-5 each turn when you're in the middle of a fight.

A sentence isn't bound to any particular length, as long as something happens in it. You could write a sentence three words long, or make a huge run-on sentence full of as many semicolons and em-dashes and parentheses as you need to fit in what you want to say.

Length doesn't need to equal impact. A 20-sentence prompt might describe a chill conversation where you're getting to know a neighbor, where a 1-sentence prompt might be 'the king has been assassinated, and you're a prime suspect.' You may use a system or table of your choice to determine the nature of an entry, or choose whatever seems like fun.

In general, you're welcome to plug this into any game you like where it'll be helpful, and any particular part of that game! Descriptions, events, character bios, equipment, you name it.

I've found using sentences as quotas works a lot better for me in my writing than word counts, and word counts are even harder to use as a measure when you're, well... playing in a format where you can't easily just plug things into a word processor to check, or don't want to. Pen-and-paper journaling in particular would be a Nightmare, lord

(This is an observation of my own writing style, so take it with a grain of salt, but I've noticed my prose sentences average between 10-16 words. It might be a good idea to try and evaluate your own average so it's easier to get an idea in advance of How Much You're Going to Be Writing for a particular prompt.)

Anyway, figured I'd post this in case it's as helpful for someone else as it's been for me. Happy roleplaying!

[mentalisttraceur-software]

I retract my previous judgement: I used to think it was a significant flaw of Git that it cannot understand any unit of difference besides "line" at its core.

For example, the "color-words" option is actually a post-processing step. Internally, git cannot record such precise diffs. If you want to look at a change which is stored in git history, differences which are more granular than a line have to be recomputed. And the tools it ships with - "git add -p", "git merge", and so on - they can't help you get any more precise than line changes.

This particularly bothered me for prose. I think git is almost a great tool for version-controlling prose. But when writing prose in a plain text format, our natural atoms of change are words and punctuation, not lines. And a line-based diff end up being huge: changing a single word is likely to cascade into a diff to the whole paragraph. Imagine trying to merge two changes to a paragraph of prose - suddenly you're back to manually comparing and picking words and characters. Note that prose includes code comments.

This also bothered me with code because code is often structured - it also has atoms of change that are not lines, which are usually much smaller than lines but can also sometimes span lines. Language-aware diffs could be profoundly useful! Just as I might sometimes say "I want a character-level diff" or "I want a word-level diff", I might say "I'd like a diff which ignores renames" or "show me a diff which ignores changes to quotes, changes to optional parentheses/braces/semicolons, and so on".

But I've come to understand that it doesn't matter if git's core has any understanding of this. Or rather, it only matters as an optimization concern.

I have the "delta" command-line program to thank for helping me realize this. See, we configure git so that delta intercepts diff output, and delta shows you nicer diff output. But the key idea is that it has its own analysis for granular changes. And it has its own analysis of the syntax of many languages - it only uses that to apply syntax highlighting, but in principle that can be generalized to static analysis that enhances diff usefulness.

After fiddling with delta for a few days, and then thinking of "git add -p" again, it hit me that all of these use-cases can be separate preprocessing or postprocessing steps. Sure, "git add -p" can't split multiple changes within one line or within adjacent changed lines, and currently that's because git's core can't understand the change more granularly - but it's increasingly clear to me that we can just work around that from the outside.

We can, for example, write a program which looks at the diff from git, applies a more granular diff within each of git's diff hunks, and lets us pick just some of those changes, then saves the other changes elsewhere, mutates the file to contain just the selected changes, and tells git to stage it. Git will record it as line deletions and additions, and sure that's a loss of information, but it's not a terrible loss of information. In principle, it's approximately always possible to unambiguously retrieve that information, so long as you have some idea of what kind of diff to try (character-level? word-level? language token level? etc). And then we even add that command as a subcommand within git, or even alias "git add -p" in our git config to call that program instead.

Basically, it now seems to me that we can entirely improve the user experience to the point where it's as if git has other diff granularities than just "line", and picks the most appropriate granularity based on the detected language, configuration, or command-line options, and that the ability to do this is trivially independent of a lack of support for it in git's core.

[grandhotelabyss]

If your second-favorite sentence in Portrait is "Her nature had, in her conceit, a certain garden-like quality..." what is your favorite? Also, any thoughts on chapter 42?

Thank you, bless you even, for taking the bait. (The question refers to my most recent Substack essay.) My favorite sentence in The Portrait of a Lady, or really just the first half of a compound sentence, is,

Deep in her soul—it was the deepest thing there—lay a belief that if a certain light should dawn she could give herself completely;

Despite forgetting the exact context, I've almost used this as the epigraph to several of my novels. Individualism so absolute it becomes its opposite, a spirit of renunciation—this is the whole of the novel, maybe the whole of James, in miniature. The "belief" and the "if" and the "could" freight the otherwise romantic sentiment with enough irony for me, but, after the semicolon, James almost coarsely punctures the romanticism, gives us the type of overt comic-ironic deflation in which novelistic prose formally specializes:

but this image, on the whole, was too formidable to be attractive.

I mentioned Michael Gorra's Portrait of a Novel in the comments to the Substack post. Gorra treats Chapter 42 as the key to the novel's importance in literary history: James's inhabitation for a whole chapter of Isabel's wandering mind moves the novel as a form from the stately analytic prose of Middlemarch to the fluid representation of consciousness in Mrs. Dalloway.

Gorra is right, but I've just reread Chapter 42—I actually haven't ever reread The Portrait of a Lady in full since I was in college; there always seems to be an unending supply of James novels to read for the first time—and I wonder if James's portrayal, at least of the mind in personal crisis, isn't more realistic than Woolf's (or Joyce's). Don't we compose interior essays when trying fully to establish how we feel about a person who isn't what we thought? Woolf and Joyce might catch the vagary of the mind walking down the street, but James's greater formality, even if less rigid than Eliot's, more in the vein of free indirect discourse, may be more appropriate to even the fevered or tortured mind in profound thought. My own representation of the inner life may in the end owe more to James than to Woolf or Joyce.

The metaphor of Isabel's imprisonment that recurs throughout the chapter suggests to me an even more profound revision of the novel: James takes the Gothic back into the psychic interior from which it emerged. Even a novel with as little "action" as this has an armature of fairy tale and popular romance, of "Bluebeard" and The Mysteries of Udolpho:

He had told her he loved the conventional; but there was a sense in which this seemed a noble declaration. In that sense, that of the love of harmony and order and decency and of all the stately offices of life, she went with him freely, and his warning had contained nothing ominous. But when, as the months had elapsed, she had followed him further and he had led her into the mansion of his own habitation, then, then she had seen where she really was.

And then there is the fine distinction Isabel inwardly draws between Osmond's European aestheticism—a means of establishing his permanent superiority over others—and her own Emersonian aristocracy of spirit, compatible with democracy (which Osmond, sounding like a Twitter reactionary, dismisses as "worthy of a radical newspaper or a Unitarian preacher"):

Her notion of the aristocratic life was simply the union of great knowledge with great liberty; the knowledge would give one a sense of duty and the liberty a sense of enjoyment.

In short, such a good book. I have to reread the whole thing, after I get to The American and What Maisie Knew and The Golden Bowl... In conclusion, here is my favorite sentence from Chapter 42, in which James takes the realist novel right back to that first of all novels, the Book of Genesis:

Under all his culture, his cleverness, his amenity, under his good-nature, his facility, his knowledge of life, his egotism lay hidden like a serpent in a bank of flowers.

[regexkind]

Every Cauchy Sequence is Bounded, a Coq Proof

AKA "wow, who'd've thought that if a sequence gets arbitrarily close together that it couldn't blow up". The proof is here. I rewrote it with comments and bullet points and some slight changes of notation.

Any surprises in the notation?

We have a weird notation for existence. We're saying "Exists K in R, K positive, and for this K there exists an N such that past that N, |g_m| <= K." (this is what AbsSmall means)

Why brackets around [0] and [<]? This is mostly to signify that these are the elements and relations from our ordered field R.

Basically we're going to use the Cauchy criterion to find that N past which all the terms of the sequence are within 1 of each other. Then we're going to show that all the terms past that point are bounded in magnitude by g_N^2 - g_N + 2.

In order for this to be an acceptable K, we need to show:

it's positive.

it's actually a bound for all g_m with m >= N.

The K-is-positive proof:

Fairly simple. 0 < 7/4, and also 7/4 <= g_N^2 - g_N + 2, because we can rewrite this inequality as 0 <= (g_N-1/2)^2.

The K-is-a-bound proof is still fairly long. We start by:

declaring that the bound is effective past N,

introducing the m in question and the fact that N<=m,

and destructing the fact that |g_m - g_N | <= 1 into two inequalities that can be used more effectively, -1 <= g_m - g_N and 1 <= g_m - g_N.

Now we split the inequality to be shown, |g_m| <= (g_N)^2 - g_N + 2, into the negative and positive components.

Here's the negative subproof, -((g_N)^2 - g_N +2) <= g_m:

To prove, this, the high-level steps were to convert this into the inequality -(g_N)^2 + 2 <= g_m - g_N, and then proving the two subinequalities -(g_N)^2 + 2 <= -1 and -1 <= g_m - g_N. The second of these is from the Cauchy criterion and the first ends up coming from rearranging to prove 0 <= (g_N)^2 + 1 based on the nonnegativity of squares and the fact that 1 is positive.

The positive subproof, g_m <= (g_N)^2 - g_N + 2, comes from:

Basically,

rearrange into g_m - g_N <= g_N * g_N + 1 - 2*g_N + 1,

and then prove that g_m - g_N <= 1 and 1 <= g_N*g_N + 1 - 2*g_N + 1.

The first of these two is just from the Cauchy criterion and the second comes from manipulating to the point where we are only showing 0 <= (g_N-1)^2, which comes from the fact that squares are nonnegative.

There are some troubling things about this proof. First, the positive and negative branches have exactly the same flavor, but the proof steps aren't "mirror images" of each other. It'd be nice if we could facilitate code reuse. If we used semicolon tactic chaining this would probably look (a) much smaller and (b) clear-as-mud, but perhaps there's a helping lemma that could be used to massage this into the appropriate format?

[engrammonline]

Mastering Grammar with Ease: A Step-by-Step Guide for Beginner Writers

Welcome to the world of grammar mastery! Whether you’re a student aiming to polish your writing skills or a professional looking to enhance your communication, understanding grammar is crucial. However, the rules can sometimes feel like a tangled web of exceptions and intricacies. Fear not! This beginner’s guide will help you unravel the complexities of grammar and set you on the path to fluent writing.

Understand the Basics Before diving into advanced grammar, it’s essential to get a solid grasp of the basics. Start with the foundational elements:

Parts of Speech: Learn about nouns, verbs, adjectives, adverbs, pronouns, conjunctions, prepositions, and interjections. Understanding these building blocks will help you construct clear and coherent sentences. Sentence Structure: Familiarize yourself with subjects, predicates, and objects. Recognize the different sentence types—declarative, interrogative, imperative, and exclamatory—and how they function. Punctuation: Master the use of commas, periods, semicolons, colons, and other punctuation marks. Proper punctuation not only clarifies your writing but also helps convey the intended tone and meaning.

Master Sentence Structure Effective writing hinges on well-structured sentences. Here are some key concepts to master:

Simple Sentences: Start with basic sentence structures. A simple sentence contains a subject and a predicate, like “She runs.” Compound Sentences: Combine two related ideas with a conjunction. For example, “She runs, and he cycles.” Complex Sentences: Introduce dependent clauses to add depth. For instance, “She runs because she enjoys the exercise.” Practicing these sentence structures will help you create varied and engaging prose.

Tackle Common Grammar Pitfalls Every writer faces challenges with grammar. Here are some common pitfalls and how to avoid them:

Subject-Verb Agreement: Ensure your subject and verb agree in number. For example, “The dog barks” (singular) vs. “The dogs bark” (plural). Confusing Homophones: Watch out for words that sound the same but have different meanings, like “their,” “there,” and “they’re.” Understanding these nuances will prevent confusion in your writing. Run-on Sentences: Avoid creating long, unwieldy sentences by using punctuation appropriately and breaking complex ideas into manageable parts.

Embrace Active Voice Active voice makes your writing more direct and vigorous. In an active voice sentence, the subject performs the action (e.g., “The teacher explained the lesson”). In contrast, passive voice can make sentences more cumbersome (e.g., “The lesson was explained by the teacher”). Use active voice to keep your writing clear and engaging.

Build Your Vocabulary A rich vocabulary enhances your writing by allowing you to choose the most precise words. Read widely, use a thesaurus, and practice incorporating new words into your writing. However, ensure that the words you choose are appropriate for your audience and context.

Practice, Practice, Practice Grammar mastery comes with practice. Write regularly, review your work, and seek feedback. Consider these tips:

Writing Prompts: Use prompts to challenge yourself and explore different writing styles and genres. Editing and Proofreading: Always review your work for grammatical errors and clarity. Tools like grammar checkers can be helpful, but they’re not foolproof—use them as a supplement, not a substitute for your own review. Reading Aloud: Hearing your writing can help you catch errors and awkward phrasing that you might miss while reading silently.

Learn from the Experts Finally, don’t hesitate to learn from others. Read grammar guides, follow writing blogs, and engage with writing communities. Consider enrolling in a writing course or workshop to further hone your skills.

Conclusion Grammar mastery doesn’t have to be a daunting task. By understanding the basics, mastering sentence structure, avoiding common pitfalls, and embracing active voice, you can significantly improve your writing. Remember, practice and continuous learning are key to fluency. With time and effort, you’ll find that writing with confidence and clarity becomes second nature.

[professoredu]

Top 5 Tips for Avoiding Run-On Sentences

1. Break Long Sentences: Divide lengthy sentences into shorter, clearer ones. Aim for one main idea per sentence.

2. Use Proper Punctuation: Ensure each independent clause is separated by appropriate punctuation (comma, semicolon, or period).

3. Utilize Conjunctions: Connect related independent clauses with conjunctions like "and," "but," "or," or "yet" to create compound sentences.

4. Employ Transitional Phrases: Introduce dependent clauses with transitional phrases like "however," "therefore," or "in addition" to enhance coherence.

5. Proofread and Revise: Review your writing for run-on sentences during the editing process. Read aloud to identify any awkward phrasing or lack of clarity.

[evilvampire]

If you see someone with a tattoo that has a very well known symbolic meaning, UNLESS IT’S USED AS A HATE SYMBOL, I don’t think it’s appropriate to ask them why they have it. Like interrogating someone with a semicolon or a Medusa tattoo about whether they’ve attempted suicide or been SA’d VS if they’re a grammar enthusiast or like Greek mythology respectively is so rude. Nobody owes you their life story.

[orlaite]

got feedback that I shouldn't use a dash with a conjunctive adverb but a semicolon like brother IDK what a "conjunctive" adverb is I barely know what an adverb is💀💀 I'm freestyling this shit IDK when it's appropriate to use any punctuation I just do it when it feels right and most of the time I get it right