We agree that I can say -1 + -1 = 0 is acceptable, because the "extremely rigourous" proof that meets your standards provided by mavromap makes the assumption 1 + (-1) = 0. So this one isn't an issue is it

Acceptable!!! lol... this doesn't have any meaning. You either accept something beacause it is proved or you do not accept it because the opposite is proved. No middle situations here.

It's more than an "assumption". That 1 + (-1) = 0" happens to be one of the axioms of the real number system so there really isn't anything that I need to prove here. However anything else you say needs proof (which I don't see). That -1 + -1 is equal to 0 or not needs a proof. The whole point of these conversation is to actually prove that (-1)(-1) = 1 so the arguments you use should either be axioms or proven propositions.

As for (-1)*(0) = 0

I don't have a problem with that. This is correct axiomatically.

The whole problem with your approach is that you try to prove: (-1)(-1) = 1 using other statements which may be obvious but in fact need proof as much as (-1)(-1) = 1 does. If they are obvious why need proof? Well (-1)(-1) = 1 is as obvious as (-1) + (-1) != 0 !!!. You say (-1) + (-1) != 0 is obvious and you use it without proof.. but you don't accept that (-1)(-1) = 1 which is as obvious and you try to prove it!!! Inconsistent..

engineers don't reinvent the wheel

I don't know about the wheel but you can surely reinvent analysis if you want. Freedom lies in mathematics afterall... However any proof of even very basic statements like (-1)(-1) = 1 must be carried out rigourously (even in your analysis).. otherwise anyone can say anything..

thank goodness the job of making the real world work is left to the engineers

No argument with that..

Here is some helpful material on the subject: http://www.calvin.edu/~rpruim/courses/m361/F03/overheads/real-axioms-print-pp4.pdf

..even an engineer who can't reinvent the wheel (very simple) can understant it. For any questions feel free to ask...

 

Acceptable!!! lol... this doesn't have any meaning. You either accept something beacause it is proved or you do not accept it because the opposite is proved. No middle situations here.

It's more than an "assumption". That 1 + (-1) = 0" happens to be one of the axioms of the real number system so there really isn't anything that I need to prove here. However anything else you say needs proof (which I don't see). That -1 + -1 is equal to 0 or not needs a proof. The whole point of these conversation is to actually prove that (-1)(-1) so the arguments you use should either be axioms or proven propositions.

I accept your point. We must be clear on two things here: 1) the OP states no strict conditions on the proofs other than the notion that it should be "theoretical" and "practical"; 2) I've never pretended my proof is complete by axioms or proven propositions, but on the basis of assumptions from others work, logic if you will.

If I had the desire I could probably sit down and give you a satisfactory analysis of the perceived shortcomings.

I don't have a problem with that. This is correct axiomatically.

The whole problem with your approach is that you try to prove: (-1)(-1) = 1 using other statements which may be obvious but in fact need proof as much as (-1)(-1) = 1 does. If they are obvious why need proof? Well (-1)(-1) = 1 is as obvious as (-1) + (-1) != 0 !!!. You say (-1) + (-1) != 0 is obvious and you use it without proof.. but you don't accept that (-1)(-1) = 1 which is as obvious and you try to prove it!!! Inconsistent..

Perhaps then I would fail a viva on the solution to -1 x -1. I also provide a proof for -ve x -ve = +ve, not -1 x -1.

Luckily for me I passed my real viva based on considerably more complex and practical mathematics than this, taking -1 x -1 = 1 as a given along the way - stone me!

I don't know about the wheel but you can surely reinvent analysis if you want. Freedom lies in mathematics afterall... However any proof of even very basic statements like (-1)(-1) = 1 must be carried out rigourously (even in your analysis).. otherwise anyone can say anything..

Indeed so, and thankfully our forefathers did this to assist science and engineering.

No argument with that..

Here is some helpful material on the subject: http://www.calvin.edu/~rpruim/courses/m361/F03/overheads/real-axioms-print-pp4.pdf

..even an engineer who can't reinvent the wheel (very simple) can understant it. For any questions feel free to ask...

Its not a case of "can't" but "won't".

These are interesting points, but I have absolutely no interest in knowing more. The real world takes these as givens and moves on.

Dave

 

I couldn't help but put in my two cents.
(you guys should encorporate LaTeX formatting into the fourms)

Given: -1 * -1 = (-1)(-1)=+1

Then we may also say that:

since

We may then cancel out the negative symbols since:

thus we have (with symbols cancled out):

Yes technically I could have cancled out the 1's aswell but that would have defeated the point I was making. This holds true for everything, like symbols cancel out. Two Positive symbols would also cancel eachother out but it still results in a positive answer because +/+ = + and -/- = +.

also note that there are more than one way to prove this, I just choose this since it is reletivly easy to demonstrate.

Note: Yes I know this thread is over with....ah welll....

 

(you guys should encorporate LaTeX formatting into the fourms)

It is - on the Post Reply window press the Sigma (∑) button and you will get a drop-down.

Dave

 

Oh awsome look at that.

 

You know, scanning through this, no one mentioned imaginary numbers, which is a valid and often used concept in electronics. Or did I miss something?

j = square root (-1)

j1 * j1 = -1

 

You know, scanning through this, no one mentioned imaginary numbers, which is a valid and often used concept in electronics. Or did I miss something?

j = square root (-1)

j1 * j1 = -1

Bill, I'm not sure how the purists would view it. The imaginary unit probably raises a whole other set of proofs...

Dave

 

I suspect this points out some weaknesses in our math system, which is an artificial construct invented by man designed as a descriptive system. The fact that the concept is absolutely required to design electronic filters validates it's concept in my mind, as it is a real world number with real world applications.

All any proof needs to collapse is one exception. Plus and minus (+ and -) aren't the only numerical signs out there.

I also like to stir. Have I mentioned I like it here?

 

I don't know if it is quite applicable, as I haven't really read what you wrote thoruoghly, but there's the a=b paradox that proves 1=2. Unfortunately you come about a divide by zero error, but you get close anyway, ohwell

 

You know, scanning through this, no one mentioned imaginary numbers, which is a valid and often used concept in electronics. Or did I miss something?

j = square root (-1)

j1 * j1 = -1

This is by definition, though, so there's nothing to prove. If you accept that j = \(\sqrt{-1}\) (or i, which I am more used to), then it follows that j\(^{2}\) = -1.

Most of the rest of this thread was concerned with a more-or-less rigorous explanation of why (-1)*(-1) equals 1, which is not by definition.
Mark

 

I don't know if it is quite applicable, as I haven't really read what you wrote thoruoghly, but there's the a=b paradox that proves 1=2. Unfortunately you come about a divide by zero error, but you get close anyway, ohwell

See: http://forum.allaboutcircuits.com/showthread.php?t=6034

Dave