We're at a loss here, anyone who can give a hint on this question? We're not asking to solve it for us...

We're at a loss here, anyone who can give a hint on this question? We're not asking to solve it for us, hints would be greatly appreciated.

are you trolling or fucking retarded

The second one, please assist.

Are you a wizard or just trolling?

Simplify to reach the equation

x_2 * x_3 = 0

That equation has two sets of infinite solutions and in either of the sets, two variables are free.

Is that based on any existing rule? We have to do it algebraic.

Are you working with numbers?

Well, numbers form groups under addition so you can add the opoosites of elements to eliminate them.

Then when you have any equation of the form a*b = 0 that implies that at least one of those variables is 0 while the other could be anything.

5*0 = 0 works
32*0 = 0
0*89 = 0

etc.

These are not rules, this is algebra.

What are you talking about? The only information in your equation says
x_1 * x_2 = 0
Now either x_1 = 0, x_2 = 0 or both are 0. Therefore there are infinitely many solutions to this problem. What do you expect?

cancel the common terms on both sides. that leaves
x2 x3 = 0

So at least one of x2 and x3 must be zero.
The solution set is therefore the union of the lines having equations x2=0 and x3=0.

It's boolean algebra.

Solution is to add one to the middle product on the left, which is in effect x1+~x1, write it out and sum it up and you can throw out the middle variable.

>He still thinks of math geometrically

The ancient greeks called, they want their limited view and weak foundation back.

Boolean algebra also works inside a field so every solution given here that works for the field of real numbers also works for boolean algebra, just change the context.

Got it! Thanks!

wat

boolean algebras are lattice objects

they can be converted into boolean rings, which have related but not identical structure

boolean rings are not fields in general Z2xZ2, what is the multiplicative inverse of (1,0)?

you are spouting nonsense.

The jerk store called. And they're running out of you.

nobody said those are real numbers

But in this problem you just need additove inverses, which must exist.

I'm not OP, just curious but could you explain this more? I looked up boolean algebra and it has a bunch of symbols that I don't see in the pic. Just so I'm clear about your solution, let me show you how I'm interpreting it. Please note this is probably completely wrong.
>add one to the middle product on the left
So is becomes [math] x_1 x_2 +(x_2 x_3 +1)+x_3 x_1 =x_1 x_2 +x_3 x_1 [/math]
Where do I go from here? Or am i misinterpreting what you are saying?

Nigga just say the solution set, aka ordered pairs or in this case ordered triples.

Geometry is kill. Algebra is where it is now.

you multiply by 1, not add as that's illegal. then 1 = x + ~x (as in any case, either of them will be 1). I'll check the thread later to see if you found the answer ;)

Oh makes sense, thanks. Here's what I'm getting:
[math] x_1 x_2 +x_2 x_3 (x_1 +!x_1 )+x_3 x_1 =x_1 x_2 +x_3 x_1 [/math]
[math] x_1 x_2 +x_1 x_2 x_3 +!x_1 x_2 x_3 +x_3 x_1 =x_1 x_2 +x_3 x_1 [/math]
[math] x_1 x_2 x_3 +!x_1 x_2 x_3 =0 [/math]
[math] x_1 x_2 x_3 =-!x_1 x_2 x_3 [/math]
[math] x_1 =-!x_1 [/math]
This can't be right. I'm still completely lost here.

> he thinks of math as sets
You are the cancer killing modern math

But that is what it is.

The answer is a set of ordered triples. Sure, you can interpret these as geometric shapes aswell but that is limiting. That is an application. You should only do this if you are working inside geometry.

If you are a mathematician working on abstract expressions then you always want to think of everything as sets until a problem DEMANDS a shift of focus to more specific interpretations.

This difference is why the greeks could not go beyond calculus of parabolas even though the jump to more complex curves was actually really easy. They were thinking in terms of fucking triangles, the cucks.

Damn bro. Might wanna brush up on your 6th grade math

What the hell is going on in this thread?

OP asked some mathematicians a question so easy that only a child can do it

The Cartesian plane... named after the ancient Greek mathematician Reneus Decartopolous.

Funny because analytic geometry pretty much enabled calculus which then enabled analysis which then allowed for rigorous formal foundation which then allowed for set theory.

Analytic geometry was the first step to get away from geometric thinking and it fucking worked.

If you are a mathematician, you are desperate for any interpretation of the objects you work with so you can have an idea of what you're doing.
You would kill just to be able to see anything that looks like a line because it's easy to manipulate.

Same question here.

Not sure if brainlets or wizards.