"What do you get when you take away 7 from 3?", I ask my daughter. "You can't do that. That's silly", she replies. "What about if I divide 5 in half?" "You get 2 in one group and 3 in the other."
Such in the world of a child, and such is the world of the natural numbers. In this world you start at zero and count 1, 2, 3 and so on. That's all the numbers you've got.
There's no problem with addition or multiplication or raising numbers to the power of something. The problems come with subtraction and division. When you try and subtract a larger number from a smaller one the answer is negative, which is outside the natural numbers. If you try to divide up a number that won't go evenly the answer is a fraction, once again outside the natural numbers.
What's 13 divided by 3? "4, and 1 remainder" in the world of the natural numbers.
The natural numbers are given the symbol: ℕ
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