studiot

The purpose of mathematical notation is to facilitate the making and communicating of statements in mathematics. It serves no other purpose and blindly attempting to redefine it simply obstructs that purpose. As that is all you have achieved so far you cannot lay claim to any such argument since you have yet to commence one. This is a complete waste of everyone's time.

Like I said, calling tha AM sidebands FM is not strictly accurate. The amount of modulation is a recoverable function (preferably one of simple proportionality) to the modulating signal. This is not the case with AM sidebands. Look at the maths.

That is not strictly accurate, as shown by my simple mathematical description in post#17

What branch of engineering? Even the best doesn't do them all.

Are you qualifying your statement about the xi s? If they are specific numbers then of course all the differential coefficients are zero, as they are for any constant. But that is introducing new material, not before stated. It is a pretty pedestrian statement that 0 + 0 + 0 + 0 +........................ = Well suprise, 0 Originally, you stated an identity concerning a bunch of variables, labelled xi This may be true for some values of xi but not for others, nevertheless it could be a valid equation. To qualify for an identity it must be true for all values of all the xi s This is elementary.

Of course there is another alternative. For the frequency modulating signal to itself be AM modulated. This is, of course, what happens in practice insofar as an audio signal continuously changes in both frequency and amplitude.

I think modern military frequency hopping radio uses an entirely different form of modulation, but if they were to use AM for the signal, frequency hopping could count as a form of combined modulation. The combination maths works like this (simplified to show the principle) Consider a carrier wave y = A cos (wct + B) y is the instantaneous total signal, which is a function of time. A = amplitude Where wc = angular frequency = 2pifc of carrier t = time In a simple unmodulated wave, A and B are constants In AM we make A variable without affecting B and In FM we make B variable without affecting A So if we introduce a second signal frequency ws = 2pifs as a second variable Ccos (wst) and C is another constant. Then we can substitute this for either A or B to obtain an AM or FM signal respectively. AM is then {Ccos (wst)} * {cos (wct + B)} FM then A cos { wct + Ccos (wst) } A combined AM~FM signal would be {Ccos (wst)} * { cos[wct + Ccos (wst)] } Now substituting either A or B is enough to convey all the carried information so why would you want to complicate matters by substituting both? Why would you be wanting to modulate with two separate modulating signals? There are other, easier ways to do this. One example of the TV signal has already been given. Another example would be the radio code data which uses a sideband. Further the limitations on the amplitude and frequency of the substituting are different and a double substitution would have to satisfy the limitations of both simultaneously.

Since this obviously interests you perhaps you would like to know that Newton's law of heat transfer states for you mixing circumstances that The rate of heat transfer is directly proportional to the temperature difference and independent of the quantity of heat. Can you make anything of that?

Why don't you try it and see? But be careful you don't scald yourself

You mean a super European DisUnion? ( OMG )10

So that's how the camel passed through the eye of the needle.

So the little boy starts by stamping his foot yet again and insulting the rest of the membership here, myself included, and ends on a typical playground threat. In my post 14 I made two comments. One was a technical one about your summation of partial derivatives, which seem to play a central role in your theory. The second was a complaint about your rude style towards others. Your response, quite reaonably, was to ask me to clarify my point. Unfortunately you failed to state which one requires clarification and I am still waiting on that. I actually (probably like others here) find your ideas interesting and am quite intrigued by the claim that the two approaches always result in the same answers. But I am assuming, with your doctorate and all, that when one of your technical statements, is challenged then you will take the appropriate technical action and reappraise it. So I say again, Quote Not so. To try to break this impasse I also offer a further explanation. There is a difference between being equal to and being identical to.

Doesn't it also depend on your definition of everything at least as much?

Not really. I just have a lot of dependents on the internet forums.

Could anyone who thinks maths can solve everything please PM me the next three week's lottery numbers. Thanx in advance.

Utter nonsense. They are European Union Beaurocracy units of economic setaside.

What you haven't told us is the context of your essay, given the title. The earliest mathematics, even such things as the requirement to measure the seasons, planetary conjunctions etc all derived from the practical or observational before the mathematics. The earliest example I can think of of mathematics preceding the application was the introduction of complex numbers in the 16th century by Cardano, some 400 years before was applied to alternating electric current theory.

What intrigues me is the "unreasonableness" part. What is unreasonable about it and why?

You misread what I wrote Counting reals means counting every real, not just focusing on two of them.

But we can (and do) include infinity in our counting. There are as many real numbers between 0 and 1 as there are on the entire real number line. This is why ordering is an important concept. Because if we count reals in order from 0 to1 we have counted an infinity of numbers.

Complex numbers and geometric vectors are not the same.

How many equations would you say this expression represents, 1 2 or 3 or more? [math] \frac{x- x_{1} }{ x_{2}- x_{1} } =\frac{y- y_{1} }{ y_{2}- y_{1} }=\frac{z- z_{1} }{ z_{2}- z_{1} }[/math]

Testing some more [math] \frac{x- x_{1} }{ x_{2}- x_{1} } =\frac{y- y_{1} }{ y_{2}- y_{1} }=\frac{z- z_{1} }{ z_{2}- z_{1} }[/math]

One thing that has not been entirely clear to me is whether you are making any distinction between collective nouns or individual nouns and if so on what basis?

According to the site information the OP has not been since since posting this. Upon rereading my post#3 I find I owe him, or her an apology for taking this thread down imaginary avenue towards complex street, fascinating though the scenery en route has been. Post#1 clearly did not envision complex numbers, indeed it is not totally clear if even the full real number system was meant. I am backtracking because in other mathematics forums there are currently debates going on as to whether numbers actually exist or can be realised in the real world. That seems to be the thrust of post#1 and the thread title. My answer is yes, any real number can, in principle, be given a place in reality.