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 June 30th, 2017, 01:29 AM #1 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 A Number is a Value or a Measure ? I hope was already proven and clear that is necessary to define a Number as a measure (and this time is not qustion of the sex of the angels...), because often, for example on a Cartesian plane X,Y, the ScaleX we choose for x and the ScaleY we choose for y, must be: $ScaleX / ScaleY =1$ or we make a mistake or we change the result (f.ex. the possibility to pass from a Sum to the Integral etc...). I'm starting to see some "result" of my Complicate Modulus work (out of y=X^n derivates).... Last edited by complicatemodulus; June 30th, 2017 at 01:32 AM.
 June 30th, 2017, 04:43 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 2,657 Thanks: 681 I have no idea what you are talking about!
 June 30th, 2017, 05:06 AM #3 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 It's a very long story, clear if you're get in contact with alexander grothendieck's work...
June 30th, 2017, 05:39 AM   #4
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Quote:
 Originally Posted by complicatemodulus I hope was already proven and clear that is necessary to define a Number as a measure (and this time is not qustion of the sex of the angels...),

Can you explain the reference to the sex of angels? Did you mean 'angles' (I wasn't aware angles had a sex, but I don't know everything...), or are you starting to go bat-**** crazy over this stuff?

Quote:
 Originally Posted by complicatemodulus ...or we make a mistake or we change the result (f.ex. the possibility to pass from a Sum to the Integral etc...)
From what little I know of your seemingly unhealthy obsession with step-sums, I don't see how you're going to come up with a meaningful result in Calculus. That is, you're talking about the scale of X and Y as though they are different when we take, for example, an integral like $\int^2_0 2x dx = 4$. I can see you saying that the scale of the Y axis is stretched to twice that of the X axis. The function $f = 2x$ is a bijection though between (0,1] and (0,2], so any mysterious and philosophical stretching of the scale of Y is done on an infinitesimal level.

If the standard order of the reals was a well-order, then $f = 2x$ couldn't possibly be bijective. The first element of (0,1] would map to the second element of (0,2], the second to the fourth, the third to the sixth, and so on. That's the clearest picture I can give. The standard order is not a well order though, as mind boggling as that is.

...just don't drive yourself insane. I've heard you mention at one point that you're risking your marriage to work on your step-sum results. She must be a good one if she puts up with being second to your number theory.

Last edited by AplanisTophet; June 30th, 2017 at 05:44 AM.

June 30th, 2017, 06:12 AM   #5
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Quote:
 Originally Posted by AplanisTophet Can you explain the reference to the sex of angels? Did you mean 'angles' (I wasn't aware angles had a sex, but I don't know everything...), or are you starting to go bat-**** crazy over this stuff?
It's probably an idiom that doesn't translate well over the language barrier.

June 30th, 2017, 07:25 AM   #6
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Quote:
 Originally Posted by AplanisTophet Can you explain the reference to the sex of angels? Did you mean 'angles' (I wasn't aware angles had a sex, but I don't know everything...), or are you starting to go bat-**** crazy over this stuff?
Don't care is a motto like "I know my chicken..." probably in english it means nothing... Yes, you can change in sex of angles and the same we can debate forever without an answer for that question

Quote:
 Originally Posted by AplanisTophet From what little I know of your seemingly unhealthy obsession with step-sums, I don't see how you're going to come up with a meaningful result in Calculus. That is, you're talking about the scale of X and Y as though they are different when we take, for example, an integral like $\int^2_0 2x dx = 4$. I can see you saying that the scale of the Y axis is stretched to twice that of the X axis. The function $f = 2x$ is a bijection though between (0,1] and (0,2], so any mysterious and philosophical stretching of the scale of Y is done on an infinitesimal level. If the standard order of the reals was a well-order, then $f = 2x$ couldn't possibly be bijective. The first element of (0,1] would map to the second element of (0,2], the second to the fourth, the third to the sixth, and so on. That's the clearest picture I can give. The standard order is not a well order though, as mind boggling as that is. ...just don't drive yourself insane. I've heard you mention at one point that you're risking your marriage to work on your step-sum results. She must be a good one if she puts up with being second to your number theory.
As told, I take my wife as far as I can from here...

All is born considering the telescoping sum property for $Y=X^n$ derivate...

In that case it don't care if you strech the scale of x, it means how far is $1$ from $0$ in the $x$, respect to how far is $1$ form $0$ in $y$.

So if you move step 1 or step 1/K, so you can make the variable exchange to $x= X/K$, than... what you know for $K\to\infty$ to the integral

The result of the Sum of the Gnomons (from $1$ to $A$), don't care how wide are gnomons, that square the curve ($Y=X^n$ derivates) is always equal to the defined integral from $0$ to $A$.

While if you try to make the same process to the $Y=1/X$ curve, respect to the gnomons given by $Y=1/\lfloor x\rfloor$, you can see that Gmonon's Area is bigger than the one bellow the $Y=1/X$ curve.

https://en.wikipedia.org/wiki/Euler%...eroni_constant

If you try to make here the process I use to pass from Sum to Integral, so you will change $x=X/K$ in the Sum (adjusting the limit as shown in my trick), you will see that the area bellow your Gnomons decreases rising $K$, till you've at the limit for $K\to\infty$ exactly the area bellow $Y=1/X$ curve.

So in other terms $Y=X^n$ derivates are characterized by $\gamma_{*} =0$

Where $\gamma_{*}$ is a new more general value (and not just Eulero's constant)

Several concernig will follows... but no time now ... I'm still working on...

More clear now ?

Last edited by complicatemodulus; June 30th, 2017 at 07:33 AM.

 June 30th, 2017, 10:00 AM #7 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 ... sorry some edit was still necessary but no time for couple of days...
June 30th, 2017, 10:12 AM   #8
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Quote:
 Originally Posted by complicatemodulus It's a very long story, clear if you're get in contact with alexander grothendieck's work...
Can you explain what you mean by this? Do you know categorical algebraic geometry? That was his field. Anyway, Je ne parle pas français.

Last edited by Maschke; June 30th, 2017 at 10:18 AM.

 June 30th, 2017, 10:34 AM #9 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 Here the picture. I'm for sure miles away from A.G. mind's level, but I very agree with him on this point since I have in the hands my own simple example: Rising $K$ the area of the Gnomons go closer and closer to the one of $y=1/x$. In the example K=1 (the difference between the areas correspond to the known $\gamma$) and K=3 (that produce a new $\gamma_{*}$ or $\gamma_{*K}$), and for $K\to\infty$ the two areas are equal and $\gamma_{\infty}=0$). So $\gamma_{*}$ is a new toy... Once again we can chose Upper Gnomons (as in the example), and Lower Gnomons and see that at the limit for $K\to\infty$ are both equal... Last edited by complicatemodulus; June 30th, 2017 at 10:39 AM.
June 30th, 2017, 10:37 AM   #10
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 Originally Posted by Maschke Can you explain what you mean by this? Do you know categorical algebraic geometry? That was his field. Anyway, Je ne parle pas français.
..and unfortunately I'm not able to read his handy hieroglyph french.... so I've just to read what is already "translated"...

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