Hairs are countable

Can you count how many hairs you have?

What you said? You can’t count the no. of hairs as it is uncountable?

Wait a minute. I can prove that you can actually count the no of hairs you have.

You don’t believe! Check it out:

I am going to use the method of induction for this.

Let n = no. of your hair(s). We need to prove that the value of n can be counted.

Basis:

Let n = 1 (i.e. you have only one hair.)

In this case, you can easily count the no. of hair you have.

Induction:

Let the proposal be true for a finite integer k. (i.e. if the no. of your hairs are <= k, you can count it. Here k is finite because the no. of hairs are also finite.)

Now we need to show the proposal is true for n=k+1.

For this just add one more hair to the pack of k hairs. As you are adding a countable no. of hairs, the pack of hair after addition remains countable.

So, the theorem is true for n=k+1.

As, k is any finite integer, the proposal is true for any finite no. of hairs. Hence the proposal is proved.

Isn’t it bizarre? It is possibly a paradox like the horse paradox (in the Horse paradox, you prove by the method of induction that all horses are of the same color.)