Is Subtraction of Real Numbers Associative or Not?

[Kocur]

Well, you might consider my remark to be really silly . 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.

 

[dextercioby]

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.

 

[HallsofIvy]

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.

 

[arildno]

Hopefully, Kocur, you've understood from the previous replies that your remark wasn't silly at all.