# theorem

1. ### Algebra Pythagorean Theorem

Hello all. I was wondering how to solve this particular problem. I am not certain I am setting it up correctly, and I think it's likely I don't have it quite right. Any help is deeply appreciated. (from textbook) "Use the Pythagorean Theorem to find the missing side length. Leave answer in...
2. ### Real analysis rudin theorem 1.21

In thorem 1.21 of Rudin He has said that as t=X/(X+1) then t^n<t<1 then maximum value of t is 1. then in the next part he has given that t^n<t<x. as maximum value of t is less than 1 why has he given that t<x ? X is a real number and 0<X and And n Is a integer n>0 .
3. ### Some sort of extension to the polynomial remainder theorem?

Two questions on another board I'd like to learn how to solve. 1) $p(x) \equiv 1 \pmod{x+1},~p(x) \equiv -7 \pmod{x+5}$ What is $p(x) \pmod{(x+1)(x+5)}$ ? 2) $x^{1000} \pmod{(x^2+1)(x+1)} = ?$
4. ### Central Limit Theorem for weighted summation of random variables?

Here is a quick question:- If X1, X2, X3,.... X20 are 20 random variables (independent/ idd) What would be the result of: 2*X1+5*X2+1*X3+18*X4...+0.5*X20? (linear combination of the random variables, with fixed known constants). Will the above function form a normal distribution if we...
5. ### Sandwich Theorem Trig Funcs.

For some reason I struggle using the sandwich theorem in solving trigonometric function limits. Example Solution But I can not understand how he does that. My try using -|Î¸| < sinÎ¸ < |Î¸| : -|2x| < sin2x < |2x| \Leftrightarrow \frac{-|2x|}{x} < \frac{sin2x}{x} < \frac{|2x|}{x} what...
6. ### Question related with Binomial Theorem

How can we find the index 'n' of the binomial \left ( \frac{x}{5}+\frac{2}{5} \right )^{n}, n\epsilon N if the 9th term of the expansion has numerically the greatest coefficient. Thx.
7. ### Mean value theorem

With the help of mean value theorem, for x>0, 0<theta<1, how we can express log(x+1){base 10} in terms of theta? The answer given is: x loge(base10)/1+theta(x)
8. ### Fermat Last Theorem Diophantine Analysis

Analysis using Diopphantine Equations Diophantine Equations are used to remove as many variables as possible and write the remaining unknowns in terms of the other unknowns. By analyzing the remaining terms as whole numbers, we can decided whether there are infinite number of solutions or zero...
9. ### Easy proof of Fermat's last Theorem

Here is a video I made of a proof of FLT. I have trouble with notation, so I made a YouTube video with handwritten equations and diagrams. 0iCRK41fOQE Enjoy the read.
10. ### Pythagoras theorem

https://en.m.wikipedia.org/wiki/Pythagorean_theorem Can we apply Pythagoras theorem to decimal points where a,b & c are decimal points sides in a right angled triangle? a^2 + b^2 = c^2 a & b are sides c is Hypothenuse Examples of a,b & c : 3.1,2.3,4.3,5.2,7.3,11.4,13.3 etc Thanks &...

12. ### Fermat's last theorem

Have I found a novel way of expressing Fermat's last theorem as follows? N = nt{ K.A^(3-p)} where N is the number of primitive triples a, b, c and a^p = b^p +c^p and a all values up to A. (K is about .155, 0.152929 for p =1 and 0.159155 for p = 2) For example, this gives for a up to 10,000...
13. ### Stokes Theorem

I am unable to solve this question of Stokes Theorem concept. It seems tough to be due to the presence of intersection of plane and sphere. Please help with the correct option and show the procedure. I am thankful in advance.
14. ### one page proof of Fermat's Last Theorem

I am sending you an invitation to see the one page proof of Fermat's Last Theorem. This proof uses Fermat's Right Triangle Theorem to prove the Theorem. Also included in the proof is the diagram Fermat could not include in the margin of the book. It is an amazing proof. wFyX5uqyLLA
15. ### series vs theorem

Hello My series is $R_3=2$ R_{n+1}=\frac{R_n}{\cos\left(\frac{\pi}{n}\right)} I will demonstrate why it is divergent. To calculate the limit from n to infinity we must first define the n, so I'm going to calculate it Can find from the formula that n = pi / arccos (Rn / (Rn + 1)) so Rn /...
16. ### Academic Guidance A lemma which is a special case of a theorem

It is often the case that a theorem is called using a lemma which in turn is an easy consequence of the theorem (in other words, is a special case of the theorem). Which term could you suggest specifically for such a lemma? I think about using my own coined word (like "specialia") to...
17. ### Binomial theorem

How can I prove the equation by using binomial theorem? Thanks.
18. ### GÃ¶delâ€™s 1st theorem is meaningless

GÃ¶delâ€™s 1st theorem is meaningless http://gamahucherpress.yellowgum.com/wp-content/uploads/GODEL5.pdf GÃ¶delâ€™s 1st theorem a) â€œAny effectively generated theory capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent...
19. ### GÃ¶del's 2nd theorem ends in paradox

Godel's 2nd theorem ends in paradox http://gamahucherpress.yellowgum.com/wp-content/uploads/GODEL5.pdf Godel's 2nd theorem is about "If an axiomatic system can be proven to be consistent and complete from within itself, then it is inconsistent.â€ But we have a paradox GÃ¶del...
20. ### GÃ¶del's theorem is invalid his G statement is banned by axiom of the system he uses

Godels theorem is invalid as his G statement is banned by an axiom of the system he uses to prove his theorem http://gamahucherpress.yellowgum.com/wp-content/uploads/GODEL5.pdf a flaw in theorem Godels sentence G is outlawed by the very axiom he uses to prove his theorem ie the axiom of...