Coming Soon!

[FrediFizzx]

No, I am not going to try again. I have already given you more than enough evidence that your claim is wrong. But you don't have to believe me. There are others who might believe you.

Hmm... I'm still waiting for any evidence at all that you are right. No evidence at all yet. None! So, I have absolutely no clue what you are talking about that you say that you have given me enough evidence. You haven't given any at all yet!
.

[local]

OK, seems we are talking past each other, because saying Total[f] = Total[g] is not the same as saying f = g.

E.g.:

f = [1,1,1]
g = [0,0,3]

Total[f] = Total[g] but nowhere is f = g, viewed either as a set or as individual values. Fred is talking about totals and Joy/local are talking about the individual values.

[Joy Christian]

OK, seems we are talking past each other, because saying Total[f] = Total[g] is not the same as saying f = g.

E.g.:

f = [1,1,1]
g = [0,0,3]

Total[f] = Total[g] but nowhere is f = g, viewed either as a set or as individual values. Fred is talking about totals and Joy/local are talking about the individual values.

It is trivial to come up with examples in which even the totals are not equal. Consider, for example f = 1 and g = 1 + cos(x). So < f > = 1 = < g >, but f =/= g, and also Total[f] =/= Total[g].
.

[FrediFizzx]

OK, seems we are talking past each other, because saying Total[f] = Total[g] is not the same as saying f = g.

E.g.:

f = [1,1,1]
g = [0,0,3]

Total[f] = Total[g] but nowhere is f = g, viewed either as a set or as individual values. Fred is talking about totals and Joy/local are talking about the individual values.

Here is 5,000 f's sorted.

Code: Select all

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[FrediFizzx]

Here is 5,000 g's sorted.

Code: Select all

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Let's see what that looks like. Scroll to the ends. Pretty similar. But they aren't exactly the same anyways so not a good example by Joy. Still no proof.
.

[FrediFizzx]

OK, seems we are talking past each other, because saying Total[f] = Total[g] is not the same as saying f = g.

E.g.:

f = [1,1,1]
g = [0,0,3]

Total[f] = Total[g] but nowhere is f = g, viewed either as a set or as individual values. Fred is talking about totals and Joy/local are talking about the individual values.

It is trivial to come up with examples in which even the totals are not equal. Consider, for example f = 1 and g = 1 + cos(x). So < f > = 1 = < g >, but f =/= g, and also Total[f] =/= Total[g].

Except for what you are saying isn't true. I've already shown that.
.

[Joy Christian]

OK, seems we are talking past each other, because saying Total[f] = Total[g] is not the same as saying f = g.

E.g.:

f = [1,1,1]
g = [0,0,3]

Total[f] = Total[g] but nowhere is f = g, viewed either as a set or as individual values. Fred is talking about totals and Joy/local are talking about the individual values.

It is trivial to come up with examples in which even the totals are not equal. Consider, for example f = 1 and g = 1 + cos(x). So < f > = 1 = < g >, but f =/= g, and also Total[f] =/= Total[g].

Except for what you are saying isn't true. I've already shown that.

You are wrong. In this example: f = 1 and g = 1 + cos(x), < f > = 1 = < g >, but f =/= g. And Total[f] = 1 but Total[g] = whatever trial number you want, so Total[f] =/= Total[g]. QED.
.

[FrediFizzx]

Except for what you are saying isn't true. I've already shown that.

You are wrong. In this example: f = 1 and g = 1 + cos(x), < f > = 1 = < g >, but f =/= g. And Total[f] = 1 but Total[g] = whatever trial number you want, so Total[f] =/= Total[g]. QED.

Now you are going to be a wise-guy and do the average of 1! Get real. We are talking about a large number of things to be averaged. If the average of f is exactly equal to the average of g, then f = g. QED.

If you are right, you should be able to find a real example online somewhere. This should also be qualified that the trials for f and g to be averaged are the same.
.

[FrediFizzx]

OK, seems we are talking past each other, because saying Total[f] = Total[g] is not the same as saying f = g.

E.g.:

f = [1,1,1]
g = [0,0,3]

Total[f] = Total[g] but nowhere is f = g, viewed either as a set or as individual values. Fred is talking about totals and Joy/local are talking about the individual values.

This borders on nonsense but I've allowed it as a really bad example. How else are f and g qualified other than by the total of their elements? And this is for a large number of things to be averaged and the number of things to be averaged should be equal for the f and g averages.
.

[Joy Christian]

Except for what you are saying isn't true. I've already shown that.

You are wrong. In this example: f = 1 and g = 1 + cos(x), < f > = 1 = < g >, but f =/= g. And Total[f] = 1 but Total[g] = whatever trial number you want, so Total[f] =/= Total[g]. QED.

Now you are going to be a wise-guy and do the average of 1! Get real. We are talking about a large number of things to be averaged. If the average of f is exactly equal to the average of g, then f = g. QED.

If you are right, you should be able to find a real example online somewhere. This should also be qualified that the trials for f and g to be averaged are the same.

I am not going to waste any more time on this. Eventually, you will figure out that you were wrong: < f > = < g > does not imply f = g, apart from some very uninteresting simple functions.
.

[FrediFizzx]

I am not going to waste any more time on this. Eventually, you will figure out that you were wrong: < f > = < g > does not imply f = g, apart from some very uninteresting simple functions.

Yep, I figured you wouldn't be able to come up with a real example. It's simple. You're wrong and I won't be figuring out that I am wrong because I'm not wrong at all.
.

[FrediFizzx]

30 million trials.



The average of f is still NOT exactly the same as the average of g. Bad example for your cause. I can easily make an example for my cause by changing Sin to Cos. But I will try to think of a better one.
.

[FrediFizzx]

If you post nonsense on this thread it will be very swiftly and mercilessly deleted!
This applies to everyone not just Gill! So, be careful of what you spew.
.

[FrediFizzx]

@gill1109 Just write out what the average of f is and what the average of g is. I don't want to see any code. Just math.
.

[Joy Christian]

.
Here is another example:

f = 1 + (x/180), with -180 < x < +180 in degrees.

g = 1 + sin(x), with x in the same range.

So < f > = 1 = < g >, but f =/= g. QED.
.

[FrediFizzx]

.
Here is another example:

f = 1 + (x/180), with -180 < x < +180 in degrees.

g = 1 + sin(x), with x in the same range.

So < f > = 1 = < g >, but f =/= g. QED.

Again, you miss the mark. With 30 million trials.



The average of f is not exactly equal to the average of g. If we were to say that they are equal, then we have to say f = g. Try again.
.

[Joy Christian]

.
I haven't missed any mark. Both < f > and < g > are exactly equal to 1, but evidently f =/= g.

In which Universe the two functions f = 1 + x and g = 1 + sin(x) are the same function?

f is a straight line and g is a sinusoidal function. But they both average exactly equal to 1.


.

[FrediFizzx]

.
I haven't missed any mark. Both < f > and < g > are exactly equal to 1, but evidently f =/= g.

In which Universe the two functions f = 1 + x and g = 1 + sin(x) are the same function?

f is a straight line and g is a sinusoidal function. But they both average exactly equal to 1.

Please demonstrate how their averages are both exactly equal to 1 when I have clearly demonstrated otherwise. You have again missed the mark.
.

[Joy Christian]

.
I haven't missed any mark. Both < f > and < g > are exactly equal to 1, but evidently f =/= g.

In which Universe the two functions f = 1 + x and g = 1 + sin(x) are the same function?

f is a straight line and g is a sinusoidal function. But they both average exactly equal to 1.

Please demonstrate how their averages are both exactly equal to 1 when I have clearly demonstrated otherwise. You have again missed the mark.

On the contrary, you have missed the entire Universe. Do the math, or look at the graph, to recognize that < f > and < g > are exactly equal to 1. No more demonstrations from me.
.

[FrediFizzx]

.
I haven't missed any mark. Both < f > and < g > are exactly equal to 1, but evidently f =/= g.

In which Universe the two functions f = 1 + x and g = 1 + sin(x) are the same function?

f is a straight line and g is a sinusoidal function. But they both average exactly equal to 1.

Please demonstrate how their averages are both exactly equal to 1 when I have clearly demonstrated otherwise. You have again missed the mark.

On the contrary, you have missed the entire Universe. Do the math, or look at the graph, to recognize that < f > and < g > are exactly equal to 1. No more demonstrations from me.

??? This looks like math to me.



Very clearly showing that you are wrong. You keep claiming no more demonstrations but you are missing the most important one for the simulation.
.