Suppose two scenarios.

In each scenario, the goal is to find the factor or rate increase from a starting value to a final value.

Scenario 1)

Suppose you currently have five dollars in the bank. Tomorrow, you deposit (that is add) ten dollars to your account. This gives you a total of fifteen dollars in your account. By what factor or rate did your account increase compared to yesterday?

The accounts value increased by a factor of 3 because 15 divided by 5 = 3. Or, in order to answer any similar problem, once can simply use the following equation:

x (unknown or factor or rate multiple) = z (final value or total banking account after money is added) / y (money added)

x = z / y

So, what were to happen if we start the initial value, 'z' at 0? Since any number divided by 0 is 0, this would return an incorrect value for x.

Scenario 2)

Your account currently has 0 dollars but you add five dollars. By what factor did your account increase?

x = 0 / 5

x = 0

As long as you don't start with 0, the pattern holds just fine. For any x greater than 0, one can computer a factor increase (or decrease) at the bank, but not when you start at 0.

So, my question is not why 0/ x = 0 but instead why this implies my bank account did not increase when surely it did. I give this conclusion because a factor of 0 increase means my account did not change - yet it did! Now, by how much?

Is it possible to know by what factor my account increases? Or is this simply the wrong question to ask?