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Are there math algebras without ZERO

Anonymous Fri 26 Jul 17:25:58 2019 No.10838791 View Reply Original Report

Quoted By: >>10838812 >>10839052 >>10839129 >>10839146 >>10840395

Many of the properties of zero seem to break algrebra under division.

Anonymous

Anonymous Fri 26 Jul 2019 17:33:06 No.10838812 Report

Quoted By: >>10838864

>>10838791
of course they do retard

Anonymous

Anonymous Fri 26 Jul 2019 17:55:12 No.10838864 Report

Quoted By: >>10838899

>>10838812
how do I avoid them

Anonymous

Anonymous Fri 26 Jul 2019 18:15:31 No.10838899 Report

Quoted By:

>>10838864
I should check to be sure, but I think that there were many times to 'mathematize' division by zero (much like complex numbers propose solutions to the square root of negative numbers). But so far, none manage to hold, as they usually make everything else needlessly harder, and are not very useful.

Anonymous

Anonymous Fri 26 Jul 2019 19:14:35 No.10839052 Report

Quoted By:

>>10838791
Lie algebras

Anonymous

Anonymous Fri 26 Jul 2019 19:22:30 No.10839069 Report

Quoted By: >>10839129 >>10839138

"Division" is just multiplying some a by b^-1 which is the multiplicative inverse of b. There is no multiplicative inverse of zero as there does not exist a real c such that 0*c=1 (you can easily prove this). So no rules of algebra are broken.

Anonymous

Anonymous Fri 26 Jul 2019 19:58:34 No.10839129 Report

Quoted By:

>>10838791
implying division exists at all is your first mistake. "division" is an algorithm based on addition and multiplication for calculating the multiplicative inverse of a number. 0 has no multiplicative inverse (see >>10839069), so the division algorithm fails.

Anonymous

Anonymous Fri 26 Jul 2019 20:03:43 No.10839138 Report

Quoted By: >>10839738 >>10839751

>>10839069
what if you add a new number that fills the role of multiplicative inverse?

Anonymous

Anonymous Fri 26 Jul 2019 20:08:38 No.10839146 Report

Quoted By: >>10839707

>>10838791
No rules are broken. Literally plot a y = 1/x on desmos. The function approaches infinity or negative infinity depend on what side x approaches 0 from. All logic.

Anonymous

Anonymous Fri 26 Jul 2019 23:56:49 No.10839707 Report

Quoted By: >>10839764

>>10839146
How do I make this formula undefined after x>2 without domain restrictions? There has to be a square root in the denominator doesn't there so it is undefined at 0 or less right?

y= -2*|x|

Anonymous

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Anonymous Sat 27 Jul 2019 00:10:29 No.10839738 Report

Quoted By:

>>10839138
Because it wouldn’t follow the division algorithm, which asserts that division of two positive integers $\frac{a}{b}$ is the statement that there exists a unique $b, q, r \in \mathbb{Z}^{+}$ for which $a = b \cdot q + r$ where $0 \leq r < b$ . So you’d have to take it up in both the existence and uniqueness ensured by the division algorithm for integers.

Anonymous

Anonymous Sat 27 Jul 2019 00:14:52 No.10839751 Report

Quoted By:

>>10839138
You'd lose associativity, which isn't worth it.

Anonymous

Anonymous Sat 27 Jul 2019 00:22:17 No.10839764 Report

Quoted By:

>>10839707
I have no clue what you are talking about. All I said you can visually see the function growing towards infinity as x approaches zero. Infinity is the limit of x as it approaches 0.

Anonymous

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Anonymous Sat 27 Jul 2019 06:31:56 No.10840395 Report

Quoted By:

>>10838791
Wheel Theory
https://en.wikipedia.org/wiki/Wheel_theory
Anton Setzer - Wheels
http://www.cs.swan.ac.uk/~csetzer/articles/wheel.pdf
Jesper Carlstrom - Wheels: On Division by Zero
http://www2.math.su.se/reports/2001/11/2001-11.pdf

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