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meemoe_uk

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Here's a math problem which I think best represents the old problem of infitesimals. Do mathy guys accept there are infinately small numbers between 0 and finite numbers? I thought some famous maths guy said there wasn`t any. If so, how do you reslove this prob?...

A rational number between 0 and 1, p ,is selected at random.

As there are an infinite number of rationals between 0 and 1, it can be shown that the chance of anyone rational being selected is 0. But we cannot deduce from this that it is impossible that a certain rational is selected, because it is possible. This has been proved for p, and as p is a variable, is prooved for all rationals between 0 and 1. So there is an infitesimal chance of selecting p. Constrast this with a number outside the boundary [0,1] being selected which really is zero chance.

So 1 / infinity is greater than 0, yeah?

A rational number between 0 and 1, p ,is selected at random.

As there are an infinite number of rationals between 0 and 1, it can be shown that the chance of anyone rational being selected is 0. But we cannot deduce from this that it is impossible that a certain rational is selected, because it is possible. This has been proved for p, and as p is a variable, is prooved for all rationals between 0 and 1. So there is an infitesimal chance of selecting p. Constrast this with a number outside the boundary [0,1] being selected which really is zero chance.

So 1 / infinity is greater than 0, yeah?

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