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 Number Theory Number Theory Math Forum

 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. Tags error, infinite, means Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post JohnnyGs Linear Algebra 5 October 18th, 2015 04:46 AM jkh1919 Calculus 5 August 4th, 2012 06:30 PM esther Calculus 1 October 25th, 2011 03:57 AM swat532 Real Analysis 3 September 15th, 2007 05:18 PM

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