Re: [Mid] A lesson in Algorism

><< Sorry, Andrew, but you're incorrect. All that results when you multiply an
> infinite sequence by 10 is that you take the decimal point and move it one
> position to the right. The sequence is *still* infinite. >>

> Never argued that point, really. It seems that some folk have not
>noticed that the number *10x* has one more digit than the number *x* and
>further that that digit is *0* and effectively curtails the series of *9*s at
>some arbitrary point (infinity minus one?). Tell me this is wrong! (if you
>can prove it, so much the better)

This is wrong. There are an infinite number of 9's. Infinity + 1 is
not greater than infinity, it still is infinity. You can't write them
all down, the numbers go on forever, by definition of saying that the
numbers go on forever.

I proved it by showing that 1/3 = 0.3333... (3's forever).

10 times 1/3 = 10/3 = 3.3333... (3's forever), because I can subtract
3 from that result and be left with the original 1/3. See? Multiply
by 10, subtract by 3, and there are no extra digits. In terms of
infinity, it just doesn't make any sense.

- Midair
From: "Charles J. Cohen" <charles@eecs.umich.edu>
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Received on Sat Jun 12 23:51:12 1999