Mathematics Database Programming Web Design Price List     Possibly the greatest paradox is that mathematics has paradoxes... Bernoulli's sophism Paradox of Bernoulli and Leibniz Paradox of even (odd) and natural numbers Paradox of Hilbert’s hotel Ross-Littlewood paradox Paradox of wizard and mermaid Paradox of enchantress and witch Paradox of Tristram Shandy Barber paradox Achilles and tortoise   With finite sets, a part is always smaller than the whole. But with infinite sets one part of the set can be just as large as the whole. Often it looks as a paradox, but from the mathematical point of view there is no paradox.

# Paradox of even and natural numbers

The Natural numbers contain even and odd numbers. However there are as many even numbers as there are natural numbers. This can be seen, by pairing natural numbers with even numbers to show that there is a one-to-one correspondence between the two sets:

 1, 2, 3, 4, 5, ... n, ...     ... ... 2, 4, 6, 8, 10, ... 2n, ...

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# Paradox of odd and natural numbers

The Natural numbers contain even and odd numbers. There are as many odd numbers as there are natural numbers. This can be seen, by pairing the natural numbers with the odd numbers to show that there is a one-to-one correspondence between the two sets:

 1, 2, 3, 4, 5, ... n, ...     ... ... 1, 3, 5, 7, 9, ... 2n - 1, ...

by Tetyana Butler Top  Complex analysis is studying the most unexpected, surprising, even paradoxical ideas in mathematics. The familiar rules of algebra and trigonometry of real numbers may break down when applied to complex numbers. Free Lessons Contact us