Prove that 3.999... = 4
(In reply to
1 = 0 ??? by Dulanjana)
Well, it looks plausible when you look at the decimal representation of the number you referenced as 0.00000...1.
But there are Aleph Null zeros between the decimal point and the 1, so what is the number?
Well, No zeros: 0.1 = 1/10;
One zero: 0.01 = 1/100 = 1/(10²);
Two zeroes: 0.001 = 1/1000 = 1/(10³);
In general: a-1 zeroes: 0.000...1 = 1/(10ª)
So Aleph Null zeroes means that the number equals 1 divided by 10 to the Aleph Null +1 power. Since Aleph Null is an infinity, 10 to the Aleph Null and 10 to the Aleph Null plus 1 are also infinities.
And once again we find we've run afoul of the "No division by zero or infinity rule.
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Posted by TomM
on 2002-08-24 09:58:46 |
re: 1 = 0 ???
