Apparently, the moderator has been "protecting" you by erasing
my posts whenever I write something that might hurt your feelings.

Doesn't that make you happy?

[QUOTE=Don Blazys;317524]The foundations of mathematics are its axioms,

which are defined as "self evident truths".

Consider the "symmetric axiom of equality"

which states that if [TEX]c=T[/TEX], then [TEX]T=c[/TEX]

and the "substitution axiom of equality"
which states that we can always substitute [TEX]\left(\frac{c}{c}\right)[/TEX] for [TEX]\left(\frac{T}{T}\right)[/TEX].

Well, if

[TEX]\left(\frac{c}{c}\right)*c^3= \left(\frac{T}{T}\right)*c^3 [/TEX] where [TEX]T=c[/TEX]

and the properties of logarithms allow the identity:

[TEX]
\left(\frac{T}{T}\right)*c^{3}=T*\left(\frac{c}{T}\right)^{\frac{\frac{3*\ln(c)}{\ln(T)}-1}{\frac{\ln(c)}{\ln(T)}-1}}[/TEX] where [TEX]T\not=c[/TEX]

then clearly, those so called

"symmetric and substitution axioms of equality"

are neither self evident, nor always true.

Think about it. If we can't always substitute [TEX]\left(\frac{c}{c}\right)[/TEX] for [TEX]\left(\frac{T}{T}\right)[/TEX],
then we must conclude that [TEX]\left(\frac{c}{c}\right)=\left(\frac{T}{T}\right)[/TEX] is not always true,
and that there do exist some identities in which [TEX]\left(\frac{c}{c}\right)\not=\left(\frac{T}{T}\right)[/TEX]
which of course shakes the very foundations of mathematics.[/QUOTE]

x/x for x = any value except 0 is asking how many groups of x go into x the answer is always 1, so t/t=1=c/c even if t!=c the reason it doesn't work with 0 is because as wikipedia has shown a/0 = x with a=0 any number of groups of 0 can give you 0 so it can take on any value, and so the value is undefined.

[QUOTE=Don Blazys;317516][COLOR=black][FONT=Verdana][COLOR=black][FONT=Verdana]Quoting "rogue":[/FONT][/COLOR]
[COLOR=black][FONT=Verdana][/FONT][/COLOR]
[COLOR=black][FONT=Verdana][/FONT][/COLOR]
[COLOR=black][FONT=Verdana]If c != T, then clearly, (T/T) != (c/c).[/FONT][/COLOR]
[COLOR=black][FONT=Verdana] [/FONT][/COLOR]
[/FONT][/COLOR][/QUOTE]

Don, do you understand your mistake on this post yet?

Assuming you do, then you need to respond to post #533.

Of course I understand my "mistake".
I am using that "mistake" to illustrate
the flaws in our axioms, and
the flaws in your reasoning.

Now, here's a simple yes or no question.

Given the identity:

[TEX]
\left(\frac{T}{T}\right)*c^{3}=T*\left(\frac{c}{T}\right)^{\frac{\frac{3*\ln(c)}{\ln(T)}-1}{\frac{\ln(c)}{\ln(T)}-1}}
[/TEX]

can we substitute [TEX]\left(\frac{c}{c}\right)[/TEX] for [TEX]\left(\frac{T}{T}\right)[/TEX] ?

Please, just answer yes or no
without any commentary whatsoever.

[QUOTE=Don Blazys;317669]Of course I understand my "mistake".
I am using that "mistake" to illustrate
the flaws in our axioms, and
the flaws in your reasoning.

Now, here's a simple yes or no question.

Given the identity:

[TEX]
\left(\frac{T}{T}\right)*c^{3}=T*\left(\frac{c}{T}\right)^{\frac{\frac{3*\ln(c)}{\ln(T)}-1}{\frac{\ln(c)}{\ln(T)}-1}}
[/TEX]

can we substitute [TEX]\left(\frac{c}{c}\right)[/TEX] for [TEX]\left(\frac{T}{T}\right)[/TEX] ?

Please, just answer yes or no
without any commentary whatsoever.[/QUOTE]No

Thanks xilman,

I agree.

On a side note, and in case you are curious,
I did make some progress on that polygonal number counting function.
A good fellow named Lars Blomberg was able to determine
the actual count w(x) all the way to x=10^15. It took him about a month
on what he said was a "state of the art processor" but it was well worth it
because with that information, I was able to greatly improve
the counting function.

Our results are posted below, and if you would like to see what the
counting function looks like at this point, then I would be happy to
post that here as well. It's really quite interesting, and as you can see,
the accuracy is remarkable.




x_______________________Actual Count____________Counting Function______Difference
10_______________________3______________________5___________________2
100______________________57_____________________60__________________3
1,000____________________622____________________628_________________6
10,000___________________6,357__________________6,364________________7
100,000__________________63,889_________________63,910_______________21
1,000,000________________639,946________________639,963______________17
10,000,000_______________6,402,325______________6,402,362_____________37
100,000,000______________64,032,121_____________64,032,273____________152
1,000,000,000____________640,349,979____________640,350,090____________111
10,000,000,000___________6,403,587,409__________6,403,587,408__________-1
100,000,000,000__________64,036,148,166_________64,036,147,620_________-546
1,000,000,000,000________640,362,343,980________640,362,340,975________-3005
10,000,000,000,000_______6,403,626,146,905______6,403,626,142,352_______-4554
100,000,000,000,000______64,036,270,046,655_____64,036,270,047,131_______476
200,000,000,000,000______128,072,542,422,652____128,072,542,422,781______129
300,000,000,000,000______192,108,815,175,881____192,108,815,178,717______2836
400,000,000,000,000______256,145,088,132,145____256,145,088,130,891_____-1254
500,000,000,000,000______320,181,361,209,667____320,181,361,208,163_____-1504
600,000,000,000,000______384,217,634,373,721____384,217,634,374,108______387
700,000,000,000,000______448,253,907,613,837____448,253,907,607,119_____-6718
800,000,000,000,000______512,290,180,895,369____512,290,180,893,137_____-2232
900,000,000,000,000______576,326,454,221,727____576,326,454,222,404______677
1,000,000,000,000,000____640,362,727,589,917____640,362,727,587,828_____-2089

Now, here's a simple yes or no question.

Given the identity:

[TEX]
\left(\frac{T}{T}\right)*c^{2}=T*\left(\frac{c}{T}\right)^{\frac{\frac{2*\ln(c)}{\ln(T)}-1}{\frac{\ln(c)}{\ln(T)}-1}}
[/TEX]

can we substitute [TEX]\left(\frac{c}{c}\right)[/TEX] for [TEX]\left(\frac{T}{T}\right)[/TEX] ?

Please, just answer yes or no
without any commentary whatsoever.

No.

Now, here's a simple yes or no question.

Given the identity:

[TEX]
\left(\frac{T}{T}\right)*c^{1}=T*\left(\frac{c}{T}\right)
[/TEX]
can we substitute [TEX]\left(\frac{c}{c}\right)[/TEX] for [TEX]\left(\frac{T}{T}\right)[/TEX] ?

Please, just answer yes or no
without any commentary whatsoever.

[QUOTE=Don Blazys;317681]Now, here's a simple yes or no question.

Given the identity:

[TEX]
\left(\frac{T}{T}\right)*c^{1}=T*\left(\frac{c}{T}\right)
[/TEX]
can we substitute [TEX]\left(\frac{c}{c}\right)[/TEX] for [TEX]\left(\frac{T}{T}\right)[/TEX] ?

Please, just answer yes or no
without any commentary whatsoever.[/QUOTE]No

[QUOTE=xilman;317720]No[/QUOTE]

Don didn't ask for it, but I will. What commentary do you have for your answer?