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Comment by veltas | Hacker News Reader

The fact that I can't even fit the real numbers between 0 and 1 on a single page, but I can fit every possible fraction in existence, doesn't mean anything?

I don't think this definition is that weird, for example by 'larger' I might say I can easily 'fit' all the rational numbers in the real numbers, but cannot fit the real numbers in the rational numbers.

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It doesn't mean anything because, with arbitrary zooming for precision, every real number is a fraction. You can't ask for infinite zooming. There is no such thing.

So, let's inspect pi. It's a fraction, precision of which depends on how much you zoom in on it. You can take it as a constant just for having a name for it.

Hi if you noticed, I never said anything about 'infinite zooming', instead I said I can write them all on the paper, which I can.

The zooming is finite for every fraction.

If infinite zooming/precision is ruled out, all real numbers can be written as fractions. Problem is with the assumption that some numbers such as pi or sqrt(2) can have absolute and full precision.

> If infinite zooming/precision is ruled out, all real numbers can be written as fractions.

How?

> Problem is with the assumption that some numbers such as pi or sqrt(2) can have absolute and full precision.

That's the least of your problems, I couldn't even draw different sized splodges per real number.

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