Question

What is the concept of zero and infinity?Are they related because both of them mean the symbol for nothing.

Answer 1

First talking about zero,

When you have some stuff, and then you give it all away, it means you have nothing. This is acceptable when you do it once or a few times and your transaction doesn't signify anything.

Now when you have to write it down, you need to have a symbol because while1-1,2-2, 1000-1000 mean the same, they might signify something different.
This gives rise to complexities. Thus the invention of 0.
(Thanks Aryabhatt, now we have one thing to boast)

Coming to significance, zero is the starting point, or the reference point of the number line.

Now, infinity.
Even this is an empty symbol.
YES. It is NOT A NUMBER BUT A SYMBOL.

Infinity might mean presence of things, which won't end.

This might be developed by the ambitious people who would like to have an endless supply of whatever they want.

We say that universe is infinite because by the time we would estimate its size, it would increase greatly.

Zero and infinity are related theoretically.
Inverse of zero is infinity.
When you divide an apple such that the size of each piece is zero, you get infinite such pieces.