1. ### Axiomatic set theory ZFC is inconsistent thus mathematics ends in contradiction

Axiomatic set theory ZFC is inconsistent, thus mathematics ends in contradiction: http://gamahucherpress.yellowgum.com/wp-content/uploads/MATHEMATICS.pdf Axiomatic set theory ZFC was in part developed to rid mathematics of its paradoxes, such as Russell's paradox. The axiom in ZFC developed...
2. ### Mathematics ends in contradiction - an integer = a non-integer

Hi. You might find this paper interesting and controversial. It proves http://gamahucherpress.yellowgum.com/wp-content/uploads/All-things-are-possible.pdf 1) Mathematics/science end in contradiction - an integer = a non-integer. When mathematics/science end in contradiction, it is proven in...
3. ### Proof by Contradiction and Counterexample

Hi, A quick question regarding proofs by counterexample, "during" proofs by contradiction. Basically, can I prove a statement P to be true, by assuming it is false (and so "not P" is true), then giving a counterexample against "not P", showing that "not P" is not always true? In other...
4. ### An issue I've noticed with algebra lately

Lately, I've been noticing a lot of contradictions, between two or more rules in algebra. One that comes to mind is the fact that radicals are considered to be a type of grouping symbol, but then the lesson tells you to simplify a radical expression and (indirectly) disregard the previously...
5. ### geometrical contradiction in rainbow formation

If the angle of incidence($i$) is such that the angle of refraction($c$) is greater than the critical angle for the water droplet, then the next angle of incidence will also be $c$ as radii of circle are equal. As the diagram shows, the light ray shall suffer total internal reflection. This...

:help: It is said that there is an infinite number (aleph 0) of elements in the set of natural numbers. If we are counting the natural numbers in such a way as to have a matching of a one-to-one correlation where n = x; for example, if the 5th element in the set of natural numbers is n = 5...
7. ### Proving that root 4 is rational by contradiction

I have done the same proof as I usually do with root 3, but for the last stage I don't know what to do: I have sqrt 4 = m/n = 4k/4l = k/l etc. Do I say that because m/n is not in the simplest form then by contradiction sqrt 4 is rational? Thanks.

Prove by contradiction that if b is an integer such that b does not divide k for every natural number k, then b=0. I know that proof by contradiction begins by assuming the false statement, therefore: there exists an integer b such that b does not divide k for every natural number k and b is...
9. ### Help needed in completing a proof

I was trying to prove the following statement (I don't know for sure whether this is true or not!) but I got stuck near the end. Please read and suggest ways for completion of the proof or even some alternative proof. Q. Prove that the least rational number which is greater than any given...
10. ### Need Help : to show 2 almost equal fraction is not equal using contradiction??

This question is taken from : https://brilliant.org/problems/same-starting-point/?group=N36CSB8k5Wpz Below shows two numbers accurate up to 4 significant figures. Which of these numbers is larger? \large \frac{122}{353} \approx 0.3456, \ \ \ \ \ \frac{75}{217} \approx 0.3456...
11. ### Proof by contradiction of linear independence

SOLUTION: proofs kill me! S=(v1,v2,...vn) is a linearly independent set of vectors in the vector space V, prove that any nonempty subset of S must be linearly independent. I know that a This is a link I stumbled upon on my travels- I understand it all, apart from the line where 0B_f+0B_g etc is...
12. ### Confused With Contradiction with Complex Exponents

Already, I was working this out, and it clearly doesn't make any sense, so let me just write it out, and please tell me where I'm going wrong: 1=e^{2Ï€i}=e^{2Ï€iln(e)}=e^{2Ï€i(1+2Ï€ik)}=e^{2Ï€i+4Ï€^2k} And, therefore: 1=e^{2Ï€i+4Ï€^2} And, that can't possibly be true, because...
13. ### Prove the followings, using the method of contradiction

How to prove using method of contradiction? a) There is no xâˆˆR such that |x-5| + |x-3| = -1 b) There is no xâˆˆR such that |x-2| + |x-3| = 1/2
14. ### FLT: A possible proof by contradiction...

Theorem: The expression x^n + y^n = z^n has no solution in positive integers x, y, z, n for any n > 2. [It suffices to prove the theorem for odd values of n > 1.] _____ Claim: x + y > z if n > 1. Proof: Substitute x + y for z and expand, obtaining x^n + y^n = (x + y)^n = x^n + P(x,y) + y^n...
15. ### Using a proof by contradiction

How can I solve this? a, b, c are integers. a is not equal to 0. If bc is not exactly divisible by a (aka there is a remainder) then b is not exactly divisible by a. By contradiction we can assume that bc is not exactly divisible by a and that b is exactly divisible by a. I start by...
16. ### a contradiction in infinite summation

While trying to find the sum of a series, I encountered a problem (the attached picture might be able to explain it in more detail). Where did I go wrong? http://postimage.org/image/57int9vtz/ Please answer. Thanks is advance.