It is the straight line that connects opposite corners.
I think it's less of a jump to claim that the ratio of this length to the side length cannot be written with a finite string than to claim that this intuitively definable length does not exist at all.
What does Wildberger think about the law of the excluded middle?
Let's play a game, we both say a number, the bigger wins, but you must talk before me and if you have the right to us ea formula, i can us a formula too. Who will win? Would this guy win against me? Would Wildberger win? If no, what the fuss with that ultrafinitist BS?
He's more of the Alex Jones of mathematics
Numbers, operations, Turing machine exists (you don't needan "infinite band". You only need a band; all the relevant information is on the table state which is finite btw and whenever a computation terminates, only a finite part of the band is used, sso everything you learn about Turing machine in CS course is legit even in ultrafinitist sick paradigm).
Mathematical proofs are as real as a computer program i.e. they are REAL and provide REAL turuth about claim, see Curry Howard correspondence.
you realize your rejection of an empirical infinity is in fact non empirical and as such is a claim based entirely upon a faith identical to that of Sasquatch believers?
>tax dollars
opinion discarded
just because mathematics can describe real things, that doesn't mean mathematics is about real things
mathematics is the logical exploration of axiomatic assumptions
>mathematics isn't about describing things that exist
And yet, virtually everybody including mathematicians themselves use math in this way in order to justify mathematical study. If you ask any mathematician about why their work is worthwhile to the public they'll say stuff about how math powers engineering, finance, etc. which are actually horrific thoughts if math is, like you say, disconnected from reality.
An even better example is when mathematicians pull stuff like Banach-Tarski out to "wow" laypeople and convince them that conservation of mass don't real. They're using the absurdity of their own results to justify their work, which is completely backwards. If a biologist got up in front of a crowd and told them they have six eyeballs, they would be laughed off the stage, but when a mathematician does the same thing it's like "Amazing! Math is so cool!"
>Banach-Tarski
ZF is inconsistent.