Hi,

Please can someone help me with this problem.

show that a,b,c are real numbers and a#0, then there is a unique solution of the equation ax+b=c.

the uniqueness of the solution is my problem.

Thank you

B

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- Sep 3rd 2006, 03:55 PMbraddyproof and rules of inferences
Hi,

Please can someone help me with this problem.

**show that a,b,c are real numbers and a#0, then there is a unique solution of the equation ax+b=c.**

the uniqueness of the solution is my problem.

Thank you

B - Sep 3rd 2006, 04:28 PMThePerfectHackerQuote:

Originally Posted by**braddy**

If,

There exists preciesly one such number such as because the real numbers form a group under addition.

Thus,

Since addition is associative we have,

Thus,

Since,

is an identity element we have,

Since, it is an element of the real numbers under multiplication and form a group. Thus, there exist a unique, such as, .

Thus,

Since, multiplication is associative we have,

Thus,

Since 1 is the multiplicative identity element we have,

- Sep 3rd 2006, 05:38 PMPlato
Here is the way that I would expect this to be done.

Suppose that each of p and q is a solution to the equation .

Then

- Sep 3rd 2006, 05:45 PMThePerfectHackerQuote:

Originally Posted by**Plato**

- Sep 3rd 2006, 06:00 PMPlato
No, you are correct!

But you showed a solution existed.

I simplified its uniqueness. - Sep 4th 2006, 11:24 PMbraddyQuote:

Originally Posted by**Plato**

:)