/sci/ - Science & Math » Thread #14281365

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Division of Additive Inverses

Anonymous Sat 05 Mar 08:14:36 2022 No.14281365 View Reply Original Report

Quoted By: >>14281375

Why does the division of two additive inverses result in a number that is not an additive inverse? Is the only reason why the division of a negative number by another negative number a positive number because we arbitrarily say it is?

Anonymous

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Anonymous Sat 05 Mar 2022 08:15:57 No.14281369 Report

Quoted By:

consequence of abstract algebra field axioms.
a prood is left to the reader

Anonymous

Anonymous Sat 05 Mar 2022 08:19:29 No.14281375 Report

Quoted By: >>14281411 >>14281485

>>14281365
You take two times the negative of -2 which is 2 and thus results in 4.

Anonymous

Anonymous Sat 05 Mar 2022 08:40:27 No.14281411 Report

Quoted By: >>14281485

>>14281375
When you multiply a number by a negative number, you additively invert the product, so when you multiply an additive inverse by a multiplicative inverse that is negative, you additively invert the product.

Anonymous

Anonymous Sat 05 Mar 2022 09:37:00 No.14281485 Report

Quoted By: >>14281527

>>14281375
>>14281411
But then, what is multiplication by a negative number?

Anonymous

Anonymous Sat 05 Mar 2022 10:21:23 No.14281527 Report

Quoted By:

>>14281485
Simple. We define a*b as f(b) where f(x)=f(x-1)+a,f(0)=0. Then -3*-2 can be calculated simply. Set g(x)=g(x-1)-3,g(0)=0. Then g(0)=g(-1)-3 which implies g(-1)=3. g(-1)=g(-2)-3 then 6=g(-2). Easy.

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