Interesting Math Facts

Paradox of even and natural numbers

Paradox of even and natural numbers

We would often think that there are more number of natural numbers than the even numbers because natural numbers is comprised of both even and odd numbers.

But can you believe that there are as many even numbers as natural numbers?

This can be proved by making one-to-one correspondence between the natural numbers and even numbers.

1 <---> 2

2 <---> 4

3 <---> 6

4 <---> 8

5 <---> 10

6 <---> 12

7 <---> 14

It goes on... In the above series, every natural number has a even number that is twice as large as it. As well every even number has a natural number that is half of it.

Here we can say that for every natural number there is equal number of even number. So its proved that both the infinite sets are same in size and are called as countably infinite.

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