Well yeah what about choice? It's true you need an axiom of choice but the idea there is a symmetry in any point between what, if we're dealing binary, anyone of them could be one. You could change but it's not about you, it's not about you. It's just that there is a symmetry at each point at each of those infinity number of points between zero and one. So in the Maths you should agree that all of them have the same status of any particular one: It's a symmetry argument.
argument about the existence of infinity in math: James Franklin vs Norman J Wildberger
Jim Franklin: "numbers are out there and exist because of symmetry."
then NJ gives an example of an infinite process that gives many different results. hence symmetry is lost.
the JIm cracks a joke about how friends of NJ who are also Aristotleans would agree with him, making NJ looks like a religious person without any rationality without providing any counter-arguments to his claim.
Well played profs
From the initial set-up by Bolzano, Cantor and Dedekind, the
twentieth century has gone on to enshrine the existence of `infinity’ as
a fundamental aspect of the mathematical world. Mathematical objects,
even simple ones such as lines and circles , are defined in terms of
“infinite sets of points”. Fundamental concepts of calculus, such as
continuity, the derivative and the integral, rest on the idea of
“completing infinite processes” and/or “performing an infinite number of
tasks”. Almost all higher and more sophisticated notions from algebraic
geometry, differential geometry, algebraic topology, and of course
analysis rest on a bedrock foundation of infinite this and infinite that.
This is all religion my friends. It is what we get when we abandon
the true path of clarity and precise thinking in order to invoke into
existence that which we would like to be true. We want our integrals,
infinite sums, infinite products, evaluations of transcendental
functions to converge to “real numbers”, and if belief in infinity is
what it takes, then that’s what we have collectively agreed to, back
somewhere in the 20th century.
In other words it's a religion of "idealistic materialism." A religion of technology as science.
https://njwildberger.com/2014/10/06/the-infinitely-real-delusion-and-my-recent-debate-with-james-franklin/
Numbers are not like that, they are just out there...All we can do is know something about them and the way to know something about them is by SYMMETRY. They have an extraordinary degree of symmetry among them. And that's one of the reason to think there is NO last one....and also the reason to thinking there's no hidden symmetry in these - meaning some existence and some less so...
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