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January 14th, 2017, 12:39 AM  #1 
Banned Camp Joined: Dec 2012 Posts: 1,028 Thanks: 24  Infinite, sometimes, means Error !
When we make: $\displaystyle \tan (\pi/2)$ we have as result: $\displaystyle \tan (\pi/2)= \infty$ This is a nice way math said us: "You're making an error: How can you compare two orthogonal values, one it's zero ?" This seems trivial, but has very, very deep consequences, for example in SET THEORY, or when $\infty$ is, for example the number of the digits of an Irrational value (like $\pi$ ). In mechanic this has a very clear results: if you try to push vertically a vagon on the rails, it never moves ahead, indipendently by the force you push on. I very like this because you can prove some theorem just saying "that since the two thinks you're talking of, are one at 90° degree to the other, there is no interaction between them". But, viceversa, when you can prove there is an interaction between two thinks (for example a bijection so a common value or serie of values I call "root/s") you can put them on other two orhogonal axis so you have a 3d graph where for example $X$ are the common values and $Y, Z$ the two results of two different operation, you can prove one depend on the other because they have the same "roots", so if one has a well known behaviour, for example a generating smooth function, you prove that also the other have the "same" smooth behaviour. I use this to prove Riemann zeros are all well sorted on the well known 1/2, but I really don't know if there already is such kind of theorem I use to prove Rh zeros are well sorted on 1/2 line... (of coruse lot of more precise concernings has to prepare the statment...) More simple:  in case of the infinite digits of the Irrational $\pi$ it said us: it's lost time to try to square the circle, for littlest and littlest measure unit (or tessel) you keep, there is no way to let you find a finite result. This told us that we have to accept that the right definition of an area is: "An Area is the result of an integral (so a limit of a Sum)" and again from here we can go deep and deep... Last edited by complicatemodulus; January 14th, 2017 at 12:44 AM. 

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