I have always had this feeling that our math is wrong. Not wrong completely, but sort of incomplete or inaccurate, in a sense that it fails to map out the universe and reality as it is. It is built on theorems one on the other, the conclusion of one theorem is the premise of another, but when you have hundreds of theorems, it feels like the entire system was broken somewhere earlier, especially after you get into calculus, it looks like the entire system has major problems.
0
I have always had the feeling that there is something wrong with the concept "zero". So if you have a situation 1-1=0, it looks good on paper, but this situation literally never happens in the real world. Things never vanish into nothing in the real world.
They either change location, or they change their structure, but they never vanish into nothing. So if you burn a piece of paper, you could say that there was a paper there, and now there isn't. But this is false, a process just happened, the process of burning, that turned the paper into ash. But the paper is still there, just in another form.
Or when you learn in kindergarten to count, they say this basket has 3 apples, if John removes 3 apples, how many apples are left there? Well 3 of course, it's just that they are in John's hands, not in the basket. In the basket there are 0, but that doesn't mean that the apples simply just vanished into nothing, they were just moved into John's hand.
So you can kind of feel, that the concept "zero" is really problematic, and it kind of reinforces this nihilistic view of the world, where everything turns into nothing, but this literally never happens.
Errors
But the problem doesn't just stop there, then you end up with other errors if you go further down the line, things like √-1 or ∞.
The √-1 basically represents incompleteness, it arises frequently when you deal with angles in trigonometry, and it always cancels out if you input the correct angle, and the equation turns into a real number.
The ∞ basically represents a process not a number. If you add 1+1+1.... together for a eternity that would be the concept of infinity, but it's certainly not a number it's a process, it symbolizes an ongoing event rather than a fixed concept.
Conclusion
It sort of looks to me like our current math system fails to distinguish between processes and concepts and they mix them together.
Luckily modern math is researched with the use of computers, where the programming language is more rational than the math description, so you can't really make many mistakes, since the computer won't let you.
You can't run a for loop forever, and say that it's a number, your computer will fry.
So luckily these misconceptions are mitigated in real testing events where we have to use finite resources to uncover the secrets of the world, any bogus math will quickly be unmasked.
But that doesn't mean that we should not pay more attention to this, some concepts may indeed be wrong.
Sources:
https://pixabay.com
