Quick question. (1 Viewer)

[Captain pi]

a>b implies a>=b

No it doesn't.

Actually, it does.

Affirmative.

It's just a little redundant (but that's fine if you're proving something specific).

 

[Estel]

I don't understand your wording. Did you mean to type "hence I set out to prove that the discriminant is >= 0"?

On that point, whilst proving that the discriminant (A) >= 0 does, further, prove real roots, so too does simply proving that A > 0. This is because positive numbers, with the exclusion of 0, are a subset of the real field. In this light, you should have realised, prior to answering, that F(x) would never have equal roots (and, therefore, A = 0) for any real m and could have, from that, sidestepped a false response. I'll, therefore, say this for the second time - the = from the >= can be omitted.

If you think so, then why don't you? You set out to prove real roots, as you say, but then you made the false statement, A >= 0 when all you needed to do was prove A > 0 for real roots. You should rethink both your initial, and your concluding statement, man, 'cause you're contradicting yourself.

I'm in no mood to argue really... my logic is completely correct and I don't feel a need to prove a point... suffice to say x>0 is a stronger inequality than x>=0, and x>0 DOES imply x>=0.
If you start with a statement "to prove roots are real, we prove discriminant >=0", you end with "discriminant = blah = blah >=0, hence the roots are real."
It is true that you can prove discriminant is > 0 in this case instead, and this rests on the logic that > 0 implies >= 0.

 

[Will Hunting]

I'm in no mood to argue really... my logic is completely correct and I don't feel a need to prove a point... suffice to say x>0 is a stronger inequality than x>=0, and x>0 DOES imply x>=0.
If you start with a statement "to prove roots are real, we prove discriminant >=0", you end with "discriminant = blah = blah >=0, hence the roots are real."
It is true that you can prove discriminant is > 0 in this case instead, and this rests on the logic that > 0 implies >= 0.

Had you paid closer attention to my wording, you would have regarded that I never brought your logic into question. I was neither debating the legitimacy of the process, nor the outcome. I was simply illustrating the misplacement of one small assumption on which you'd founded your reasoning.

Dude, whether or not you're in the mood for an argument or feel the need to prove a point changes neither the error in your judgment, nor the error in your deduction. I agree with you on the notion that concluding statements should echo intial statements, however, you should not have made the particular initial statement that you did in this case - that's all. I'm not launching into this again, so I'll leave you with that to chew on.

 

[Will Hunting]

Affirmative.

It's just a little redundant (but that's fine if you're proving something specific).

Negative, SIR! lol

You have incontrovertibly confused a > b implies a >= b with a >=b implies a > b. The former is senseless. a > b reads a is greater than b. This means a cannot equal b, because a is greater than be for all a and b. To come from yet another angle, a is greater than b and is NOT equal to b. The latter is true, since if a can equal b and a can also be greater than b, then, of course, a can be greater than b.

You may return to your quarters, captain. Dismissed.

 

[Ogden_Nash]

You have incontrovertibly confused a > b implies a >= b with a >=b implies a > b. The former is senseless. a > b reads a is greater than b. This means a cannot equal b, because a is greater than be for all a and b. To come from yet another angle, a is greater than b and is NOT equal to b. The latter is true, since if a can equal b and a can also be greater than b, then, of course, a can be greater than b.

Hold on, If a >= b, how can you say that this implies a > b, considering the case when a = b?

 

[Slidey]

a>b implies a>=b, because a>b is a subset of a>=b.

Think of it this way:
a>b is a subset of a>=b. I think you agree with this, yes?
Since it is a subset, that means that it has a superset which contains both it AND other things. This superset is a>=b, which contains also a=b. Therefore, if it is true that a>b, then it is also true that a>=b (even if a never equals b).