Math ASCII Notation Demo

Mathematical content on Apronus.com is presented in Math ASCII Notation which can be properly displayed by all Web browsers because it uses only the basic set of characters found on all keyboards and in all fonts.

The purpose of these pages is to demonstrate the power of the Math ASCII Notation. In principle, it can be used to write mathematical content of any complexity. In practice, its limits can be seen when trying to write complicated formulas (containing, for example, variables with many indexes or multiple integrals).

Despite its limitations the Math ASCII Notation has much expressive power, as can be seen from browsing through these pages.

What is a disjoint sequence of sets?
{A[n]} sequence of sets
for all natural m,n, m!=n
A[m] and A[n] are disjoint
Prove that an increasing sequence of sets converges.
The limit is equal to the union of all the sets from this sequence.
Prove that a decreasing sequence of sets converges.
The limit is equal to the intersection of all the sets from this sequence.
Prove that a disjoint sequence of sets converges.
The limit is the empty set.
Let A,B c X.
Let 1(A) denote the characteristic function of the set A.
Prove that the two functions are equal:
1(A+B) = ???
1(A+B) = |1(A) - 1(B)|
Let A[n] c X for all natural n.
If AcX, then let 1(A) denote the characteristic function of the set A defined on X.
/\x:-X 1(lim_inf A[n])(x) = ???
/\x:-X 1(lim_inf A[n])(x) = lim_inf 1(A[n])(x)
Let A[n] c X for all natural n. Let AcX.
If HcX, then let 1(H) denote the characteristic function of the set H defined on X.
(1) the sequence of sets {A[n]} converges to the set A
(2) the function 1(A[n]) converges pointwise to the function 1(A)
page 13
first measure theory notebook
(A\B) u (B\A) = ???
Express differently.
(A\B) u (B\A) = (A u B) \ (A n B)
(A u B) \ (A n B) = ???
Express differently.
(A u B) \ (A n B) = (A\B) u (B\A)
Is it true that
(A + B) c (A + C) u (C + B)
?
Yes.