mersenneforum.org - Standard crank division by zero thread

mersenneforum.org (https://www.mersenneforum.org/index.php)

- Miscellaneous Math (https://www.mersenneforum.org/forumdisplay.php?f=56)

- - Standard crank division by zero thread (https://www.mersenneforum.org/showthread.php?t=15278)

[QUOTE=Don Blazys;254365]
You are wrong. Here's why...

Given [TEX]\frac{T}{T}[/TEX] and substituting [TEX]c[/TEX] for [TEX]T[/TEX] results in [TEX]\frac{c}{c}[/TEX].

Given [TEX]\frac{T}{T}[/TEX] and substituting [TEX]\frac{c}{c}[/TEX] for [TEX]\frac{T}{T}[/TEX] [B][I][U]also[/U][/I][/B] results in [TEX]\frac{c}{c}[/TEX].

So clearly, the two substitutions are absolutely equivalent!
[/QUOTE]

Now you are confusing implication with equivalence! I do not see any point in arguing anymore as it is clear that we are not following the same logic.

[QUOTE=Don Blazys;254365]
Journals are dead.

They are quickly going the way of the horse and buggy and
exept for a few elitist snobs, nobody reads them anymore.

Most people [B][I]now[/I][/B] get their information by searching the internet,
and when they search for "Beal's Conjecture Proof", it is [B][I]my[/I][/B] proof,
which is [B][I]obviously[/I][/B] both true and correct, that they will find!
[/QUOTE]

Most people might search information from the internet. But those who do not want to check all the details, refereed journals are still the way to go (and most of them are online). It is true that papers in refereed journals contain lots of errors, but (for example) arXiv contains surely more. Random web pages on the internet on the matters at hand are almost sure to contain errors.

[QUOTE=Don Blazys;254365]
However, if it turns out that [TEX]\alpha[/TEX] in this function precisely matches
the most accurately measured value of the fine structure constant,
then my counting function will be of that much greater importance to mankind.

Doesn't that make you happy? :smile:
[/QUOTE]

You did say that the approximation is logically derived. So assuming you telling the truth one can indeed approximate fine structure constant by the counting function and there is no reason to verify that they match.

However, as I am not asleep, dreaming does not make me happy. To be honest, your previous illogical responses make me seriously doubt that there is any such logical derivation. If there is no derivation, any computation beyond the known measurements for the fine structure constant give no new information about the constant.

Quoting science man 88:[QUOTE]
here's an example proving you wrong lets say T=1 and c=2
[/QUOTE]

Sorry science man, but in my proof, [TEX]T[/TEX] is [B][I]defined[/I][/B] as being an element of [TEX]\left{2,3,4...\right}[/TEX].

Thus, we can not allow [TEX]T=1[/TEX].

My proof is correct.

Don.

[QUOTE=Don Blazys;254371]Quoting science man 88:

Sorry science man, but in my proof, [TEX]T[/TEX] is [B][I]defined[/I][/B] as being an element of [TEX]\left{2,3,4...\right}[/TEX].

Thus, we can not allow [TEX]T=1[/TEX].

My proof is correct.

Don.[/QUOTE]|Let T = 2 and c =3

[QUOTE=xilman;254372]|Let T = 2 and c =3[/QUOTE]

continuing with this under these new values:

T[TEX]\ne[/TEX]c but 2/2=3/3=1 so T/T = c/c=1 which you say can't happen which is false.

check about some things on https://oeis.org/A0904

On this page : we have the formula for the nth k-gonal, if accurate and the comment about using k and n values such that [TEX]k\ge 3[/TEX] and [TEX]n\ge 3[/TEX] by making a Pari script that made it look like a table I think I have a way using a finite sum of linear equations based on the 3-gonal sequence to calculate the amount of polygonal numbers of order greater than 2 less than a value x and I have an idea to sort out the one final thing. Anyone care for details? Note this post is technically talking of a special equation to calculate a value(function ?) and therefore can fit into this thread.

formula given:

[QUOTE]The n-th k-gonal number is 1 +k*n(n-1)/2 - (n-1)^2.[/QUOTE]

PARI:

[CODE]for(k=3,100,for(n=3,10,print1(1+k*n*(n-1)/2-(n-1)^2","));print(":"k))[/CODE]

[QUOTE=science_man_88;254378]On this page : we have the formula for the nth k-gonal, if accurate and the comment about using k and n values such that [TEX]k\ge 3[/TEX] and [TEX]n\ge 3[/TEX] by making a Pari script that made it look like a table I think I have a way using a finite sum of linear equations based on the 3-gonal sequence to calculate the amount of polygonal numbers of order greater than 2 less than a value x and I have an idea to sort out the one final thing. Anyone care for details? Note this post is technically talking of a special equation to calculate a value(function ?) and therefore can fit into this thread.

formula given:

PARI:

[CODE]for(k=3,100,for(n=3,10,print1(1+k*n*(n-1)/2-(n-1)^2","));print(":"k))[/CODE][/QUOTE]

okay anyways I'm moving on this idea and it stems from the fact that the nth k-gonal numbers are on the line ((n-1)th 3-gonal) *z + (n-th 3-gonal) so the maximum ( assuming it repeats) number of k-gonal numbers of k and n greater than or equal to 3 are a finite sum of the number of results in these sequences less than x until the y-th 3-gonal number where y is the highest n such that (y 3-gonal) <x

[QUOTE=Don Blazys;254365]Given [TEX]\frac{T}{T}[/TEX] and substituting [TEX]c[/TEX] for [TEX]T[/TEX] results in [TEX]\frac{c}{c}[/TEX].

Given [TEX]\frac{T}{T}[/TEX] and substituting [TEX]\frac{c}{c}[/TEX] for [TEX]\frac{T}{T}[/TEX] [B][I][U]also[/U][/I][/B] results in [TEX]\frac{c}{c}[/TEX].

So clearly, the two substitutions are absolutely equivalent![/QUOTE]

Are you off your rocker?

If c = 2 and T = 3, then (c/c) * c^2 = 4. Substituting c = T makes this equation false. Substituting T/T for c/c leaves it true. The two are not only inequivalent but obviously inequivalent.

[QUOTE=CRGreathouse;254401]Are you off your rocker?

If c = 2 and T = 3, then (c/c) * c^2 = 4. Substituting c = T makes this equation false. Substituting T/T for c/c leaves it true. The two are not only inequivalent but obviously inequivalent.[/QUOTE]

what do you think of my idea ( so far in my search I've found too many repeats ( though all of 3-gonal numbers so far)).

[QUOTE=science_man_88;254410]what do you think of my idea ( so far in my search I've found too many repeats ( though all of 3-gonal numbers so far)).[/QUOTE]

I've solved the repeat part I realized I could use the vecsort features.

The problem now is speeding it up.

[CODE]blazy2(x)=y=[];for(k=3,x+1,for(n=3,x+1,if((1+k*n*(n-1)/2-(n-1)^2)<(x+1),y=concat(y,[(1+k*n*(n-1)/2-(n-1)^2)]),break(1))));y=vecsort(y,,8);return(#y)[/CODE]

as far as I'm willing to calculate with this slow function it matches with the first table second column values at the link at the start of the thread.

To: rajula,

Quoting rajula:
[QUOTE]Now you are confusing implication with equivalence![/QUOTE]

No rajula, it is [B][I]you[/I][/B] who is confused.

The terms containing [TEX]T[/TEX] are [B][I]identities.[/I][/B]
Thus, if [TEX]Z,z>2[/TEX], then we [B][U]can't[/U][/B] substitute
[TEX]c[/TEX] for [TEX]T[/TEX], or [B][SIZE=3][COLOR=red]equivalently[/COLOR][/SIZE][/B], [TEX]\frac{c}{c}[/TEX] for [TEX]\frac{T}{T}[/TEX].

The substitutions being equivalent [B][I]implies[/I][/B] that
we cannot substitute [TEX]\frac{c}{c}[/TEX] for [TEX]\frac{T}{T}[/TEX] if and only if [TEX]Z,z>2[/TEX].

Without that [B][I]equivalence[/I][/B], there would be no [B]implication ![/B]

Again, you seem to be insisting that we can substitute
[TEX]c[/TEX] for [TEX]T[/TEX], or [B][SIZE=3][COLOR=red]equivalently[/COLOR][/SIZE][/B], [TEX]\frac{c}{c}[/TEX] for [TEX]\frac{T}{T}[/TEX] on the left side only,
without taking into account that such a substitution would
automatically [B][I]contradict[/I][/B] the [B][U]fact[/U][/B] that the terms involving
logarithms were [B][U]derived[/U][/B] from the terms showing [TEX]\frac{T}{T}[/TEX].

Quoting rajula:
[QUOTE]
So assuming you telling the truth one can indeed approximate fine structure constant by
the counting function and there is no reason to verify that they match.
[/QUOTE]
I disagree. There are plenty of reasons to verify that they match!
[B][I]Any[/I][/B] theory, regardless of whether it is the result of luck, logic or both,
is only as good as it can [B][I]predict[/I][/B] experimental results and [B][I][U]must[/U][/I][/B] therefore be
tested, and [B][I]verified[/I][/B] in that regard! That's how science progresses.

If a determination of say, [TEX]\varpi(10^{18})[/TEX] allows us to [B][I]predict [/I][/B]several more digits of
the fine structure constant and those predictions are then corroberated by physical experiments,
then that would constitute [B][I][U]evidence[/U][/I][/B] that polygonal numbers are somehow related to quantum mechanics.

Quoting rajula:
[QUOTE]
However, as I am not asleep, dreaming does not make me happy.
[/QUOTE]
Well, I think you [B][I]are[/I][/B] asleep. You sure have been posting like it.

Quoting rajula:
[QUOTE]
I do not see any point in arguing anymore as it is clear that we are not following the same logic.
[/QUOTE]

On that we can agree. :smile:

Don.