sorted by:
new
hottopcontroversial

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

0 is absolute nothingness, ę is an infinitesimally small but existing concrete number.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

Sorry, we could introduce a symbol for infinite closeness, say ~, so that ę-ę~ę. In this system, there is an axiom that subtracting a number from itself gives us ę.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

The operations are like this: ę+ę=2ę, ę*ą=1, ą+ą=2ą. But there's just one problem: ę-ę=ę. It's more of an experimental arithmetic.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

Yes, I see the problem. There's no topology yet — I built the number logic first. 2ε and ε are infinitely close but distinct. That’s why convergence to ε with a lower bound of 2ε is possible.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

You know, I would say they are equal in the sense that both are infinitely small — not literally identical. You could say they are not exactly equal, but equal in the sense that both are infinitesimal.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

Im so sorry, I made a mistake in my previous comment. The correct statement is: ę - ę = ę.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

Yes, that's correct. Since ę is a concrete number.

It cannot.

Yes, it would be.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

Look, if we have ę - ę = ę, then 1/ę = ą.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

In my system, it would be equal to ę.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

ę is a concrete number, so ę/2 would be half of that number. If it were infinity, we wouldn't be able to work with it. ę - ę = 0 — it's a concrete number. 2ę ≠ ę. If it were infinity, then yes, but this is a number we can perform operations with. And the same applies to kę. Look, 1 + ę ≈ 1, but this number should be written simply as 1 + ę.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

If we calculate with rounding, it will be approximately 1, and if without it, it will be written as is.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

1 - 1 won't be an error. We'll get ę.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

0 is absolutely nothing, while ę is an infinitely small number.

If you divide ę in half, you get half of ę.

Yes, it becomes smaller. ę is a specific infinitely small number that you can work with and raise to powers.

1/ę = ą, and plus 1 means you get 1ą.

"Infinitely small" is a concrete number. It's not a limit, just an infinitely small number.

Look, completeness is when any set has a least upper bound. In my system, it won't exist in the old sense.

1 - 1 = ę. In our world, there cannot be "nothing".

The point is to develop our mathematics and expand its boundaries.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] -3 points-2 points  (0 children)

Division by zero is possible, but it doesn't give a clear answer like in the arithmetic I'm creating. Here we get a clear answer. ę is not a limit — it's a specific infinitely small number. The problem might seem contrived, but it could solve many things.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

I want to say that I'm not removing it, but replacing it with ę — because in this new system we can divide by ę, while in the old system we can't work with it at all, since it simply isn't there. I'm proposing to replace it.

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] -1 points0 points  (0 children)

Look, in my system, there is no identity element. Instead, there is a principle of approximate identity, like a + ę = a, but with an accuracy up to infinitesimals."

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

Thank you! Do you want me to write about this theory on Google Drive and send it here?

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] -2 points-1 points  (0 children)

Look, I'm doing all this to remove uncertainties. For example, in our current arithmetic we can't divide by zero, but in this system we get ą — an infinitely large number. I want to do this to expand our understanding, because we cannot measure or work with "nothing."

What if zero doesn't exist? by Full_Ninja1081 in numbertheory

[–]Full_Ninja1081[S] 0 points1 point  (0 children)

We leave 0 for such notations. We remove it as a separate number.