Zero is a perfect number, but zero is also a dangerous number. Many things can horribly go wrong with zero and you must really careful when you handle it. There is something that you cannot do with zero : you can’t divide something by zero or you can’t have thing like zero to the power of zero. And I was asked for this all the time from my younger brother, “Why can’t I divide by zero, I want to divide by zero and it’s infinity.. bla bla bla..” I’ll show him why we can’t divide by zero and it’s not just infinity, it’s more complicated than that.

Let’s take a look at multiply, if you want multiply 10 by 5, you can do it by add 10 to 10 five times. And division is opposite to multiplication, that’s mean when you divide 20 by 4, you subtract 4 from 20

0+10=10 20-4=16

10+10=20 16-4=12

5 times 20+10=30 5 times 12-4=8

30+10=40 8-4=4

40+10=50 4-4=0

But now if I divide by zero, that means I subtract something by zero over and over, let’s try 10 divided by 0 :

10-0=10

10-0=10

infinity 10-0=10

10-0=10

………

So it takes infinity times to divide 10 by zero, but you cannot say something equals to infinity; it’s like you say 1+1 = Green. And now my brother argue that there’s nothing wrong writing 10=infinity. Here’s why, if 10=infinity and 20=infinity, does that mean

10=infinity= 20

and therefore I can say 1=2 ? That’s nonsense.

And now it’s time to calculus get involved, if we take the limit of 1x as x goes very close to zero

limx→01x=infinity

In this case, we can basically say that 10=infinity, but we have 2 different answers for this problem. As x goes to zero from the right, we have positive infinity and negative infinity if x goes from the left.

What about 00 (zero to the power of zero) ?

The other thing that my brother gets very annoy about is...