Using axioms for proof

T13

How would I go about using axioms of rational numbers to show that x^2 > 0 if x is a rational number? :s-smilie:

Reply 1

james22

16

Do you mean the axioms of arithmetic? If not then what are the axioms you can use.

Reply 2

T13

OP

Original post by james22

Do you mean the axioms of arithmetic? If not then what are the axioms you can use.

Yeah the axioms for arithmetic :smile:

Reply 3

james22

16

Can you show that a*b=b*a? Can you show that -1*-1=1? If so then the rest of the proof is fairly easy.

EDIT: You also need to show that the positive real numbers are closed under multiplication.

There may be a quicker way to do this but i can't think of any that start of scratch.

(edited 12 years ago)

Reply 4

T13

OP

Original post by james22

Can you show that a*b=b*a? Can you show that -1*-1=1? If so then the rest of the proof is fairly easy.

EDIT: You also need to show that the positive real numbers are closed under multiplication.

There may be a quicker way to do this but i can't think of any that start of scratch.

Erm...I know that positive real numbers are closed under multiplication but I dont know the other bits

Reply 5

james22

16

Original post by T13

Erm...I know that positive real numbers are closed under multiplication but I dont know the other bits

To get you started say -1*-1=a

Then consider what each side of the following equals:

-1*(1+-1)=-1*1+-1*-1

We can do this because it is an axiom of multiplication that brackets can be expanded like this.

As for a*b=b*a I don't know I'm afraid.

Using axioms for proof

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