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Order the natural numbers as follows: Now let F be a continuous function from the reals to the reals and suppose p≺q in the above ordering. Then if F has a point of least ...

The tangent numbers, also called a zag number, and given by T_n=(2^(2n)(2^(2n)-1)|B_(2n)|)/(2n), (1) where B_n is a Bernoulli number, are numbers that can be defined either ...

The tetrix is the three-dimensional analog of the Sierpiński sieve illustrated above, also called the Sierpiński sponge or Sierpiński tetrahedron. The nth iteration of the ...

Trigonometric functions of npi/7 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 7 is not a ...

Turing machines are defined by sets of rules that operate on four parameters: (state, tape cell color, operation, state). Let the states and tape cell colors be numbered and ...

A technical mathematical object which bears the same resemblance to binary relations as categories do to functions and sets.

A set which transforms via converse functions. Antisets usually arise in the context of Chu spaces.

Axiomatic set theory is a version of set theory in which axioms are taken as uninterpreted rather than as formalizations of pre-existing truths.

The cardinal number of any set is lower than the cardinal number of the set of all its subsets. A corollary is that there is no highest aleph (aleph).

sum_(k=0)^m(phi_k(x)phi_k(y))/(gamma_k)=(phi_(m+1)(x)phi_m(y)-phi_m(x)phi_(m+1)(y))/(a_mgamma_m(x-y),) (1) where phi_k(x) are orthogonal polynomials with weighting function ...