/sci/ - Science & Math

All right /sci/, I want to explore the stars and for that we need a math revolution to solve certain problems in physics, and one of the most important problems to solve is division by zero. We'll start by taking Brahmagupta's idea that any real number divided by zero is merely expressed a R/0. So, 1÷0=1/0, etc.

What's important to note is that zero factorized numbers do not obey conventional wisdom when it comes to mathematical operations. As an example, I assume most of you know of this "paradox" which supposedly proves division by zero is impossible:

X = Y
X^2 = XY
X^2 - Y^2 = XY - Y^2
(X + Y)(X - Y) = Y(X - Y)
Factor out X - Y from both sides
X + Y = Y
Since X = Y, you can say:
Y + Y = Y
2Y = Y
2 = 1

The supposed genius solution to this is that when you factor out X - Y, since X and Y have equal values then X - Y = 0, this it's a division by zero, which is the reason we arrive at a nonsense answer. Rather, the issue here is that the division by zero was done improperly. Instead, it should read as:

(X +Y)/0 = Y/0

And no, you can't factorize those. Why? Well, if you did, it would mean 1/0 + 1/0 = 2/0. But it doesn't. See, you're used to adding fractions this way, but a better way to express fractional additions would be:

1/X + 1/Y = (X+Y)/(XY)

This is true of all fractions where the numerator is one. Now, let's try it with 1/0 + 1/0:

(0+0)/(0*0)

Which means that adding two numbers with an equal numerators factorized by zero equals 0/0. So clearly, conventional wisdom does not apply to numbers factorized by zero. In fact, if we add real numbers, we get an interesting observation:

1/0 + 1/2 = 2/0
1/0 + 1/3 = 3/0
1/0 + 1/4 = 4/0
etc.

Meaning, the smaller the real number we add to 1/0, the higher the numerator of the result.

So, we have a some basics here. Everything seems to challenge common mathematical beliefs, but patterns and logic emerge from it. This means there is a structured, sensible way to divide by zero.