Mathematical Induction Without Dominoes

How to actually understand Mathematical Induction

Imagine you want to show that the number 5 has a certain property. Let’s say this property is that the sum of all natural numbers up until 5 (0, 1, 2, 3, 4 and 5) is equal to

Now you could just add 0, 1, 2, 3, 4 and 5 together and show that this sum equals 15, which is also what the above fraction gives.

But you could also assume the property holds for the number 4, and work from there to show it also holds for 5.