[MOVED] Proving x * 0 = 0, using field axioms

[futurewrench]

Can anyone tell me, or just get me started on proving that x.0=0 using only axioms? i think i'm supposed to use the additive identity x+0=x axiom, then the distributive property x(y+z)=(xy)+(xz) and then additive inverse x + (-x) = 0

But I'm having some trouble...

help!

 

[stapel]

Re: x.0=0 axioms!

Can anyone tell me, or just get me started on proving that x.0=0 using only axioms?

What is the meaning of "x-point-zero"? What axioms have you been given?

Thank you.

Eliz.

 

[futurewrench]

x.0 meaning x times 0

the axioms i gave above are probably the only ones i need to use...but i have a list of about 15...things like x.y=y.x or x+y=y+x

 

[stapel]

x.0 meaning x times 0

Thank you.

the axioms i gave above are probably the only ones i need to use.

If you've already completed a proof using just those axioms, that's great. But if not, then it might help to know what else you have to work with. (Different books present different axioms by different names in different orders, so we can't make assumptions regarding what you have to work with.)

Thank you.

Eliz.

 

[pka]

Here are the field axioms:

1. For each a and b in the field, a + b is in the field.[/*:m:boairx6t]
2. For each a and b in the field, a + b = b + a.[/*:m:boairx6t]
3. For each a, b, and c in the field, a + (b + c) = (a + b) + c.[/*:m:boairx6t]
4. There is an element 0 in the field such that a + 0 = a for each a in the field.[/*:m:boairx6t]
5. For each a in the field, there is an element, -a, in the field, and a + (-a) = 0.[/*:m:boairx6t]
6. For each a and b in the field, a * b is in the field, and a * b = b * a.[/*:m:boairx6t]
7. For each a, b, and c in the field, a * (b * c) = (a * b) * c.[/*:m:boairx6t]
8. There is an element 1 in the field such that, for all a, a * 1 = a.[/*:m:boairx6t]
9. For each a in the field, a not 0, there exists an a^-1 such that a * a^-1 = 1.[/*:m:boairx6t]
10. For each a, b, and c in the field, a * (b + c) = a * b + a * c.[/*:m:boairx6t]

 

[stapel]

Note: Your (post-calculus) abstract-algebra thread has been moved from pre-calc algebra to "Advanced Math", and the subject line has been clarified.
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Hint: Start with "x * 0". Then note the existance, by Axiom 8, of "1". Rewrite "0", using "1" and Axiom 5. Then apply Axiom 10. Then apply Axioms 5 and 8 again, to get the desired result.

Eliz.