Determine whether the given sets are open, closed, neither open nor closed, or both open and closed. 1. the union of all the closed intervals [-1+1/n, 1-1/n],...
[-1+1/n,1-1/n] is a closed set but the enumerable union of a closed set is not always closed and this union tends to ]-1,1[ so it's an opened set the...
... set is not always closed and this union tends to ]-1,1[ so it's an opened set ... second one is open I think the intersection of a *finite* number of open...
Hi, I need help with this problem. Use Zorn's Lemma to show that if B and B' are bases for the vector space V, then there exists a bijection \phi : B -> B'. ...
... Let (S,f) denote any subset S of B along with an injective function f: S --> B', such that (B-S) U f(S) (that is, the union of the complement of S in B and...
can any one give prrof of the following parts of theorem 1-we have ab=0 if and only if a=0 or b=0 or both 2-we have a0 and b0 if and only if ab0...
Hi,A few weeks ago I introduced the amazing formula x^(1/x) - 1 ~ log(x)/x. This in turn gives us the number of prime numbers < x = Pi(x) ~ 1/(x^(1/x)-1). This...
Hi, Here are some more interesting consequences of my nth root quest. Find the convergent to the recurrsion x = 1/(x^(1/(x+1)) - 1) for any x> 1. Find the...
"There are 100 people at a party.Each person has an even number ( possibly zero) number of acquaintances.Prove that there are three people at the party with...
... Indirect proof: There are 50 even numbers between 0 and 99 (inclusive). Assume there are not 3 people with the same number of acquitances. Then the 100 ...
Here's a not too hard, fun problem: Person A and B play the following game: 27 tokens are on the table, and each player take turns taking anywhere from 1 to...
Hi All I found out cool Math tricks and shortcuts to solve problems very quickly and perform great at exams and SAT. These are really interesting to...
Hi All I found out cool Math tricks and shortcuts to solve problems very quickly and perform great at exams and SAT. These are really interesting to...
Hey all... Sorry I haven't been online in months due to changing and shifting responsibilities and interests (and even then that's a vast understatement and...
Excuse me ,but these methods shown on the links are called VEDIC MATHEMATICS in india.In our 'scriptures' the vedas, these methods are mentioned.So these arent...
Hi Clooneman, I don't think that's going to work in general. When five tokens are left there are 22 tokens divided between the two (A & B) piles. Who wins at...
This solution is not correct. For example, what if when you get down to 5, you each hold an even number of tokens? (This is possible because 27 - 5 = even.)...
The \Delta operator of a sequence a_n is \Delta a_n=a_{n+1}-a_n. The \Delta operator is defined as E-I where E is the right shift operator Ea_n=a_{n+1} and I...
Hi sarthak Yes, you are absolutely correct. These tricks are a part of something they call 'Vedic Math' in certain South Asian countries. Infact the source of...
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