As a programmer I always have to take great care that nowhere in the code something is divided by zero (x/0). I consider the fact that our mathematical system does not allow such a basic operation a major flaw.

The root of the problem is, as I see it, the claim that
1 = 1 and therfor
1 + 1 = 2 or that
1 – 1 = 0.
Behind this claim, which goes through all mathematical thinking, is the idea of constancy and/or equality. That one thing should be equal to itself from one instant to the next or that there indeed should be two things that have in any way completely equal properties.

Mathematics aims to reduce all the properties of an object to only the ones that matter for a certain calculation and tries to make calculations based on these abstractions before putting them back to the object or objects in question claiming that the result is in some sense “correct”.

I’d like to give an example that illustrates the problem:

Imagine you need or desire a bicycle. But you have no money. You look around and soon you find a job were you are paid 8 MU/h (read monetary units per hour and fill in which ever currency you prefer).

The price of the bicycle you want is 35 MU. A quick calculation tells you that you need to work for 35 / 8 = 4.375 hours. Great! Next morning at 8 am you are there, you skip all the breaks and at 12:22:30 you go to the boss to get paid.

The boss, an otherwise reasonable man, gives you 32 MU, telling you that he only pays full hours, no exception made.

Grinding your teeth you take the 32 MU and go to the bicycle shop. There you find your bike. You ask for a discount explaining to the clerk your problem, but he is unyielding, so for the moment the value of your 32 MU is, in terms of how many bikes you can buy, zero.

But luck is on your side, you discover that one of the bikes has a little scratch to its frame and the clerk gives in. You get the bike for 32 MU. The clerk, who all the time thought he had 2.0 bikes realizes he only had 1.9143. You have in terms of functionality 1.0 bikes and not only 0.9143. So while you bought 1.0 bike only 0.9143 were sold.

You may now (correctly) protest, that the boss only counts the property “hour” not the properties “minutes and seconds”, that you count the number of functional bikes while the clerk counts some monetary equivalent to the products he sells, so everybody in this story calculates different properties of certain objects and therefor comes to different results. But as I will show, it is not as easy as that.

To be continued…