Wikipedia
real number system proof : Lambert (1761) gave the first flawed proof that cannot be rational; .... The affinely extended real number system adds two elements + and . ..... More from Wikipedia
real number system proof : Like the real number system, the complex number system is a field and is ..... results concerning transcendental numbers were Lambert's 1761 proof that ..... More from Wikipedia
Complex Numbers
Introduction - Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex ..
Introduction - Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex ..Introduction
Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex number h..
Consider a simple quadratic equation x 2 + 1 = 0. There is no real number which satisfies this equation. So there was a need to find a system which could answer to this problem. Euler used the symbol 'i' to denote to solve the above equation. Complex number h.. !!! There is nothing illegal - it's just a clever (unknown) trick !!! Force Zero System Working Casinos can be found on my site: www.TheRouletteCracker.net.tc FORCE THE ZERO! The Method is based on an electronic failure on a random computer programme installed into (internet and electronic terminals). The random programme installed into these systems which distributes the numbers is only random within its probability quota. What Does This Mean? The random programme installed into machines ...
Please don't say it is by "chance" or by the 'Big Bang' that we have the world we know about. Fibonacci number, From Wikipedia : In mathematics, the Fibonacci numbers are a sequence of numbers named after Leonardo of Pisa, known as Fibonacci. Fibonacci's 1202 book Liber Abaci introduced the sequence to Western European mathematics, although the sequence had been previously described in Indian mathematics. The first number of the sequence is 0, the second number is 1, and each subsequent ...
Question : how would i find a 1-1 correspondence between the interval [0,1] and the interval [a,b] for any a,b in R.
I guess it means i need to find the correspondence that is one-to-one and onto.
Thank you for input. thank you all for input..i solved the problem :)
Answer : In both intervals the number of real numbers is infinite. Let's say you have a point x in [0,1], then you want to take the distance between 0 and x (which would be x), find what it would be proportionally in [a,b] and apply that distance to be the distance between a and x', where x' is the mapped image of x. To get proportionality between [0,1] and [a,b] you have to multiply by (b-a), then shift by a to start at a. So you get x' = (b-a)x + a I'll let you prove that it's 1-1. PS: you could also have a reverse map x' = b - (b-a)x.. More from Yahoo Answers
Answer : In both intervals the number of real numbers is infinite. Let's say you have a point x in [0,1], then you want to take the distance between 0 and x (which would be x), find what it would be proportionally in [a,b] and apply that distance to be the distance between a and x', where x' is the mapped image of x. To get proportionality between [0,1] and [a,b] you have to multiply by (b-a), then shift by a to start at a. So you get x' = (b-a)x + a I'll let you prove that it's 1-1. PS: you could also have a reverse map x' = b - (b-a)x.. More from Yahoo Answers
Question : Definition: Let f be a real function defined on E. We say that
f(t) -> A as t -> x,
where A and x are in the extended real number system, if for every neighborhood U of A there is a neighborhood V of x such that V n E is not empty, and such that f(t) is a member of U for all t is a member of V n E, t does not equal x.
Prove Theorem 4.34 (Rudin)
Let f and g be defined on E. Suppose
f(t) -> A, g(t) -> B as t -> x,
Then
(a) f(t) -> A' implies A' = A,
(b) (f + g)(t) -> A + B,
(c) (f..
Answer : Well, if you can't come up with a better idea, just prove it separately for the cases where you're talking about real numbers and where you aren't. In fact, you should be able to do that in most cases by invoking the analogous facts about limits as defined in high school/calculus. ;).. More from Yahoo Answers
Answer : Well, if you can't come up with a better idea, just prove it separately for the cases where you're talking about real numbers and where you aren't. In fact, you should be able to do that in most cases by invoking the analogous facts about limits as defined in high school/calculus. ;).. More from Yahoo Answers
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