Re: Gabriel's Theorem - what I have learned thus far.

From: David C. Ullrich (ullrich_at_math.okstate.edu)
Date: 02/20/05 

Date: Sun, 20 Feb 2005 13:14:59 -0600

On 20 Feb 2005 07:55:37 -0800, "Jason" <logamath@yahoo.com> wrote:

>Fool,
> At college they teach you that constant functions are differentiable.
>Does this mean it is true just because some professor says it is?!

No, that's not the reason. The reason is it's incredibly easy to
prove.

> Do
>you know what differentiable means?
>Has it ever been well-defined? Does it makes sense to say that a
>tangent to a tangent line is the line itself? This is what they tell
>you in college - you twit! How can a tangent be the whole line
>itself?!

Ah, so we finally see the reason you object to constants being
differentiable.

>This is absurd, for by definition a tangent to a curve touches
>the curve exactly in one point.

No, that's not the definition of "tangent line".

But there you are using the word "touch" again. This time
it's you, not Gabriel<g>. You need to give us the _definition_
of this word, otherwise you're not making any sense.

>Differentiable: Hmmm, let's see. The common point of intersection is
>the classic 'derivative' definition. Newton would be haviing a good
>laugh at stupid fools the liek of you. He found the finite difference
>quotient in an attempt to *approximate* tangent gradients at first. The
>approximation later became a definition when the *fathers* of real
>analysis threw in a limit and call it the derivative. Why did they do
>it? They would probably also be having a good laugh. The main reason
>was to get the wretched religious clerics off their backs. What better
>way to do it - devise a difficult and obscure way to explain limits and
>the ultimate quotient and what do you get? Real Analysis! Ha!
>
>But I know how an insecure boy like you will react. Go on then, let's
>see if I am right...

************************

David C. Ullrich

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