Re: Cantor Confusion

Han de Bruijn wrote:
True, but you are ignoring Virgi's adjective "sound". Calculus existed
way back during the time of Newton and Leibniz, but you could hardly
call their use of the infinite and infinitessimals at all "sound" by
today's standards. It wasn't until Bolzano and Weierstrass made things
truly rigorous in the 19th century was Calculus anywhere near sound.

Allright. And they should have _stopped_ at this point in time.

I agree. And what's with these people saying the Earth is round?
Geez, they are going too far. Next thang you know, they'll be pushin'
them thar evolution to our kids!

There was a pre-emptive war. Set Theory invaded Calculus.

A sneak attack it was too. Like Pearl Harbor. Damn ruskies.

Even infinitessimals were consistently defined by Robinson.

I've never seen such useless things as Robinson's infinitesimals.

Anything too small to see ain't real, anyone knows that.

With the
exception of Aristotle's Logic and Euclid's Geometry, much of
mathematics would not be considered acceptable by today's standards.

Who's "standards"? The problem with standards is that you have so many
to choose from. Are you imposing _your_ standards upon the rest of us?

Yeah, it's just discrimination, I tell ya. Like wearing shoes or
counting teeth! We don't need standards in mathematics! Speaking of
which, what's the latest definition of pi these days?

Even Guass and Euler played a bit fast and loose (although they were
considered impeccably precise in their day.)

Huh? Would you say that absolute nitwits like Zermelo and Fraenkel, who
have contributed nothing to actual mathematics, are greater individuals
than Gauss and Euler? Did I really read this? Can't believe my eyes ...

None of them fer-ners ain't no damn good nohow!

In ancient times, arithmetic was discovered in much the same way
physical laws were. "Hey, notice that when we do this, that always
happens..." As centuries of very hard work, mathematicians have boiled
arithmetic assumptions down to some basic axioms, and all of the
remaining theorems flow forth.

I prefer the good ol' days, where the men were men, the sheep were
nervous, and Mathematics had no axioms. Tracking your assumptions
seems like an invasion of privacy to me anyway. (It's the NSA doin'
it, I tell ya.) What business is it of yours what assumptions I make?
Hell, Russell's paradox never harmed me none.

.

Relevant Pages

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