#but they're only the same up to isomorphism | Explore Tumblr posts and blogs

femme-objet · 2 years ago

Text

i understand: what i'm bringing up is that given the very very long list of mathematical structures for which this (assigning each element to a number) is possible, what is it ontologically that determines which are numbers and which aren't? why do we say any random cauchy sequence is not a number, but special equivalence classes of them are? and my point is essentially your last paragraph: we rely on cultural assumptions as to what it means to "quack like a number" when we make the separation between the two, as is done for this tournament

Number Tournament: SIX vs STAR

[link to all polls]

6 (six)

seed: 9 (47 nominations)

previous opponent: thirty-nine

definition: the number of sides of both a regular shape that tiles the 2D plane as well as a regular shape that tiles 3D space

{0|0} (star)

seed: 41 (12 nominations)

previous opponent: twenty-four

definition: a fuzzy value from combinatorial game theory. it's very imnportant to understanding the evaluation of different positions in impartial games, games where actions are not restricted to either player

#i would also argue that there's no single thing as a 'number'#not only because a real number is not the same mathematical object as an integer #but also (as always) because of benecerraf's identification problem #we say that real numbers constructed through dedekind cuts are the same as real numbers constructed through cauchy sequences #but they're only the same up to isomorphism #is there a philosophical distinction to be made between the two?#should we consider sets between which there is an isomorphism to be the same?#id say a number is like a worm #there are definitely things that you can look at and say thats a worm #but many of those things are completely unrelated other than through the fact that they're animals

581 notes · View notes

rotationalsymmetry · 2 years ago

Text

these tags tho:

#we say that real numbers constructed through dedekind cuts are the same as real numbers constructed through cauchy sequences#but they're only the same up to isomorphism

#is there a philosophical distinction to be made between the two?#should we consider sets between which there is an isomorphism to be the same?

#id say a number is like a worm#there are definitely things that you can look at and say thats a worm#but many of those things are completely unrelated other than through the fact that they're animals

from @femme-objet