# Show that A + 0 = A

• May 1st 2010, 10:39 AM
gary223
Show that A + 0 = A
Just a simple question I want to know how to do, google hasn't been a help.

Show that A + 0 = A

Is it something like, make A a 1 so its 1 + 0 = 1?
• May 1st 2010, 10:40 PM
aman_cc
Quote:

Originally Posted by gary223
Just a simple question I want to know how to do, google hasn't been a help.

Show that A + 0 = A

Is it something like, make A a 1 so its 1 + 0 = 1?

You need to be more specific now. What is A, 0, +? I presume there is nothing to prove here. It is an assumption we start with. And the above holds by definition of 0.
• May 2nd 2010, 04:37 AM
sirius0
For all A

A+0=A

Kind of self obvious but to prove like less obvious equalities perhaps the below is helpful

Transpose to A-A=0
• May 2nd 2010, 04:59 AM
kompik
Quote:

Originally Posted by gary223
Just a simple question I want to know how to do, google hasn't been a help.

Show that A + 0 = A

Is it something like, make A a 1 so its 1 + 0 = 1?

Is A a matrix? If so, are you working over arbitrary field, over reals...?

Nevertheless, to verify this for matrices you just have to look at each position, you get equality $a_{i,j}+0=a_{i,j}$, which is valid in any field (in particular, in reals).

However, it was just a guest that you mean matrices - you should have specified the context of your question.
• May 8th 2010, 08:08 AM
gary223
Its not a matrix. I'd imagine it has something to do with Boolean algebra?
• May 8th 2010, 11:13 PM
Drexel28
Quote:

Originally Posted by gary223
Its not a matrix. I'd imagine it has something to do with Boolean algebra?

How about $A\vee 0=A\vee \left(A\wedge \neg A\right)=A$ by the absorption property?
• May 9th 2010, 03:06 AM
HallsofIvy
Quote:

Originally Posted by gary223
Its not a matrix. I'd imagine it has something to do with Boolean algebra?

You imagine? This is your problem! Where did you get it? What algebraic system are you in?