Is Subtraction of Real Numbers Associative or Not?

  • Thread starter Thread starter Kocur
  • Start date Start date
  • Tags Tags
    Confusing
Kocur
Messages
12
Reaction score
0
Well, you might consider my remark to be really silly :smile:. I was thinking about subtraction of reals and the following ideas came to my mind:

From one side, we may consider subtraction to be addition of the inverse of an element, for example:

(5 - 3) - 2 = (5 + (-3)) + (-2).

This "version" of subtraction is associative and (5 + (-3)) + (-2) = 5 + ((-3) + (-2)).

On the other side, if we treat subtraction separately from the addition, it is not associative:

(5 - 3) - 2 is different from 5 - (3 - 2).

Kocur.
 
Physics news on Phys.org
Yes,it's actually the "+" operation (called addition) that comes into abstract fields,rings and algebras definition.

As u can check,"+" is an associative operation.

Daniel.
 
In general mathematicians do not consider "subtraction" to be a distinct operation- largely because it would not be associative and associative is a very nice property.
Subtraction is simply shorthand for "add the additive inverse" and, of course, addition is associative.
 
Hopefully, Kocur, you've understood from the previous replies that your remark wasn't silly at all.
 

Thread '##(A/\mathfrak{a})_{\mathfrak{p}/\mathfrak{a}}## and its isomorphism?'

I asked online questions about Proposition 2.1.1: The answer I got is the following: I have some questions about the answer I got. When the person answering says: ##1.## Is the map ##\mathfrak{q}\mapsto \mathfrak{q} A _\mathfrak{p}## from ##A\setminus \mathfrak{p}\to A_\mathfrak{p}##? But I don't understand what the author meant for the rest of the sentence in mathematical notation: ##2.## In the next statement where the author says: How is ##A\to...
View full post »

Thread 'Questions about non existence of GCDs vs (coimages, cokernels)'

The following are taken from the two sources, 1) from this online page and the book An Introduction to Module Theory by: Ibrahim Assem, Flavio U. Coelho. In the Abelian Categories chapter in the module theory text on page 157, right after presenting IV.2.21 Definition, the authors states "Image and coimage may or may not exist, but if they do, then they are unique up to isomorphism (because so are kernels and cokernels). Also in the reference url page above, the authors present two...
View full post »

Thread 'Trouble understanding an online solution to an exercise in Dummit & Foote'

##\textbf{Exercise 10}:## I came across the following solution online: Questions: 1. When the author states in "that ring (not sure if he is referring to ##R## or ##R/\mathfrak{p}##, but I am guessing the later) ##x_n x_{n+1}=0## for all odd $n$ and ##x_{n+1}## is invertible, so that ##x_n=0##" 2. How does ##x_nx_{n+1}=0## implies that ##x_{n+1}## is invertible and ##x_n=0##. I mean if the quotient ring ##R/\mathfrak{p}## is an integral domain, and ##x_{n+1}## is invertible then...
View full post »

Similar threads

MHB T31 vector subtraction is not commutative and not associative.
Replies
5
Views
1K
A Near-Rings with Noncommutative Addition and Two-Sided Distributivity
Replies
4
Views
2K
I Is subtraction an operation on Z?
Replies
10
Views
3K
I Quintic Polynomial Tschirnhaus Transform: Possible complex Bring Radicals
Replies
0
Views
2K
B Commutative & Associative property of negative numbers
Replies
4
Views
3K
I Dfns group action & group, written in terms of the other
Replies
26
Views
374
A Anti-dual numbers and what are their properties?
Replies
1
Views
2K
MHB Algebraic Structure to solve a linear system of 2 variables?
Replies
5
Views
3K
A "The Operation Combination Problem"
Replies
2
Views
2K
I Modulo and Modulus in math and computer programming
Replies
5
Views
3K

Hot Threads

Recent Insights

Back
Top