Re: Simple fact

In article <1184918446.539300.205200@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
<commentchecker@xxxxxxxxxxxx> wrote:
Guys

Say a and b are real numbers.

How do we show that the inverse additive of (a+b) is -b+-a

Start by NOT writing "+-a".

Write either -a-b, or else (-b) + (-a).

It'll be great if we can use group theory to do so.

You're the guy who thinks you will build up a child's confidence by
"slip[ping] in some group theory", right?

Shouldn't you at least understand the subject first? You are heading
straight into the disaster of New Math, with teachers trying to teach
what they don't understand.

As to your question:

The additive inverse of X is the UNIQUE element that, when added to X,
yields 0.

So, if you want to show that (-b)+(-a) is the additive inverse of
(a+b), then take (a+b), add (-b)+(-a) to it, and verify that you get
0.

After that how can we show that

inverse additive of countable sum of real numbers are the sum of each
of the inverse

So -(a1+a2+a3+...)=-a1-a2-a3...

How?

Induction.

And please, stay away from the kids and don't try to teach them any
group theory for now.

--
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"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
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Arturo Magidin
magidin-at-member-ams-org

.