Logo_Math
Suitcase of Dreams
Math, database, programming, graphics, web design
Logo_Integral
Mathematical paradoxes
Possibly the greatest paradox is that mathematics has paradoxes...
Complex functions paradoxes
Infinity paradoxes
Set theory paradoxes
We will add more

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, ...
pairing numbers pairing numbers pairing numbers pairing numbers pairing numbers ... pairing numbers ...
2, 4, 6, 8, 10, ... 2n, ...

Top


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, ...
pairing numbers pairing numbers pairing numbers pairing numbers pairing numbers ... pairing numbers ...
1, 3, 5, 7, 9, ... 2n - 1, ...

by Tetyana Butler

Complex functions Tutorial
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

Copyright © 2006 Suitcase of Dreams All rights reserved.