Imagine you can see the whole Number Line and every one of the infinite individual points it comprises. Imagine you want a quick and easy way to distinguish those points corresponding to rational numbers from the ones corresponding to irrationals. What you're going to do is ID the rational points by draping a bright-red hankie over each one; that way they'll stand out. Since geometric points are technically dimensionless, we don't know what they look like, but we know that it's not going to take a very big red hankie to cover one. The red hankie can in truth be arbitrarily small, like say .00000001 units, or half that size, or half that half, etc. Actually, even the smallest hankie is going to be unnecessarily large ...I hope you enjoyed imagining an infinite number of infinitely small red hankies as much as I did.
Wednesday, September 13, 2006
More brilliance
(p89):
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2 comments:
uf. well bob, this post definitely got a laugh from rich, as i read it out to the lad laid out luxuriantly on the sofa, but even though i was the one actually reading it, you lost me on the 2nd sentence and by the end, my brain felt as if some very confusing tremors had been set scribbling through it. hence, uf, my exclamation of choice. x
Oh, let the sexy math words flow over you...
(Ooer.)
Would it help if I added that at the end of this section is added the following paragraph:
"Let's each pause privately for a moment to try to imagine what the inside of Professor G. F. L. P. Cantor's head might look like as he's proving stuff like this."
I guess not, but that gave me a chuckle too. xXx
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