Is this a valid maths proof?

[killari]

I wouldn't say that's too much better than the op as a proof as you haven't justified why d can only = 0 if the numerator = 0 or the denominator = +- infinity.

A better and more elegant way would be to prove by contradiction:

so by contradiction if a /= 0 then d /= 0.

In all fairness I would say that your proof is far less complete than mine. Firstly I used a contradiction technique to disprove the OP's original hypothesis.

Secondly, a statement of proof by observation is completely acceptable for trivial and intuitive processes. Something like 0/(anyrealnumber/{0}) = 0 could have been included, but I'm sure you'd agree that it is hardly worth stating. Something with regards to x being infinite may be required for a 'not so technical maths course'.

Thirdly your statement didn't cover the other necessary constraints.

 

[frying_pan_cat]

In all fairness I would say that your proof is far less complete than mine. Firstly I used a contradiction technique to disprove the OP's original hypothesis.

Secondly, a statement of proof by observation is completely acceptable for trivial and intuitive processes. Something like 0/(anyrealnumber/{0}) = 0 could have been included, but I'm sure you'd agree that it is hardly worth stating. Something with regards to x being infinite may be required for a 'not so technical maths course'.

Thirdly your statement didn't cover the other necessary constraints.

I do agree that your proof is more complete than mine and should have been clearer about that in my post. I just thought that given the triviality of the statement being proved your statement of proof by observation was not much more precise than just stating that d \= 0 as an observation

 

[killari]

I do agree that your proof is more complete than mine and should have been clearer about that in my post. I just thought that given the triviality of the statement being proved your statement of proof by observation was not much more precise than just stating that d \= 0 as an observation

I wouldn't say it was AS trivial, it definitely explains enough for the proof to make sense. I see what you're getting at but I don't think the extra steps were necessary.