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Don't believe that pi is a real number 
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#1
Mar614, 10:41 PM

P: 392

Wiki defines a real number as
Admittedly, though in order to give a real rigorous proof that pi is not real, we would need a rigorous definition of real number, something much more precise then represent the quantity and we don't have that yet. 


#2
Mar614, 10:46 PM

P: 9

Pi is real, just irrational as well because you can graph it, it's real like try graphing i (or the square root of 1), that's when numbers get imaginary
Oh imaginary numbers.... Gotta love math sometimes :D 


#3
Mar614, 10:49 PM

P: 1,622

[tex] \pi = 2\int_{1}^1 \sqrt{1x^2} \; \mathrm{d}x [/tex] So I am confused where you are getting all these wild ideas from since everything I just mentioned is very standard stuff. 


#4
Mar614, 10:50 PM

P: 392

Don't believe that pi is a real number



#5
Mar614, 10:55 PM

P: 9

I should clarify,
Put it on a number line *beautiful demonstration*  5 0 5 .i, or sqrRt(1) *note, i is on its own, because i is an introvert no really though I just doesn't follow logic, therefore it's not on the line 


#6
Mar614, 10:59 PM

P: 392

If you cannot, then I'll give you mine and you can analyze my definition. A perfectly rigorous definition starts with a group of indefinable words. The axioms tell us the true and false combination of these indefinables. Every definition is built up from these indefinables. A perfectly rigorous (aka decidedable) sentence is then justified when it can be broken down into a group of sentences which are all composed of indefinables and each sentence has already been declared true but the axioms. For example, say you start with the indefinable words: x, y, z, R, S, T, & Then you have a new sentence: gh FG ui You break that sentence down into: xRy & zSx & yTx Those three sentences are already declared true by the axioms. So the new sentence gh FG ui is a perfectly rigorous definition. I seriously doubt there is such a perfect definition as to what Dedkind cuts are. I could be wrong and I'm willing to listen. 


#7
Mar614, 11:01 PM

P: 392




#8
Mar614, 11:03 PM

P: 9

You're never gonna be perfect, but with 5 trillion digits, I think you are going to be fine in a practical sense at that point you start to run out of molecules in the paper to be so precise!



#9
Mar614, 11:07 PM

Mentor
P: 18,051

Basically, you are given some collection of wellformed formula's, called axioms. And you are also given inference rules which allow you to go from one wellformed formula to another. A perfectly rigorous proof is now a list of wellformed formulas. Every wellformed formula follows from a previous one by either an axiom or an inference rule. Giving definitions of real numbers and giving definitions of pi is then perfectly possible. Also, claiming that pi is not a real number counts as crackpottery and is not allowed on this forum. 


#10
Mar614, 11:08 PM

P: 392




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