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Author(s): Michal Ryszard Wojcik
Other collections by the author:

No. of items: 1505
Rating:
Last updated: Apr 28, 2003

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 Description

This is my personal mathematical collection. It is not a commercial product designed for a generic user. The collection is full of references to my notes in my notebooks. It is incomplete without my notebooks. Very often, the answer is simply the number of a page in my notebooks.

I decided to publish my collection in order to inspire other people to use SuperMemo for mathematics. This collection can be downloaded for free.

Michal Ryszard Wojcik
(MEE how RISH uhrd VOY chick)

 Sample

Q: In the extended real number system, why can't we define: oo+(-oo)=0?
A: Because then we could prove that oo+(-oo)=7 by using associativity.

A: 1) oo+(-oo)=0
A: 2) 7+[ oo+(-oo) ] = 7 + 0
A: 3) [7 + oo] + (-oo) = 7
A: 4) oo + (-oo) = 7

Q: Investigate the uniform convergence of
Q: f[n](x) = sqrt(n) * x * (1-x*x)^n on [0,1].
A: No uniform convergence on [0,1].
A: Use: x[n] = 1 / sqrt(n)

A: If 0<M<1, then uniform convergence on [M,1].

Q: What is a ring of sets?
A: Let X be a set. Let R c P(X).

A: R is a ring of sets
A: iff
A: (1) R is nonempty
A: (2) A,B :- R => A u B :- R
A: (3) A,B :- R => A \ B :- R

Q: Let a[n] be a decreasing sequence of positive numbers.

Q: (1) the series a[n] converges
Q: (2) the series 2^k * a[2^k] converges

Q: Prove that (1) <=> (2).

A: page 58 in the first analysis notebook

Q: Express differently:

Q: max(x,y) = ???

A: max(x,y) = ( x + y + |x - y| ) / 2

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 MRWmath, (SM2000 format or later, 378 KB) Download time: 1 min @ 56 Kbps

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