Re: universal quantification, because g⤨(g⁻¹(x)) = g(y) [1/2] Re: how

On 5/11/2024 7:11 PM, Ross Finlayson wrote:

On 05/11/2024 02:44 PM, Ross Finlayson wrote:

On 05/11/2024 02:05 PM, Ross Finlayson wrote:

On 05/11/2024 12:24 PM, Jim Burns wrote:

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The case is that induction goes through,
an inviolable law you call it:
does it go all the way through?
Does it complete?

It is complete.
There is no completing.activity,
so I wouldn't say it completes.
Compare to right triangles:
Are all the squares of two shorter sides
summed to the square of the longest side?
That's a tricky question to answer because
there is no summing done.
That relationship between the sides
is simply something true about right triangles.
And it is complete == it is true for each.
We don't typically ask the tricky question
about right triangles.
We ask the tricky question about cisfinite induction
because we imagine it as a process,
which we don't for right triangles.
Cisfinite induction is NOT a process.
Cisfinite induction is an argument,
completely correct or completely incorrect.

See, the contrary inductive analyst just says
"in case you don't have a deductive argument why
something is so, induction is so much shifting-sands
and slippery-slope." He just has "the base case is
you haven't completed induction, and so is the
subsequent case, case closed: case not closed".

When the argument is completed,
induction is completed.
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There is something completely different
which is also called induction.
The completely.different induction is physics.
Physics.induction is not unbreakable.
Physics.induction isn't cisfinite or transfinite induction.