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The prime link 05-0201, illustrated above, with braid word sigma_1^2sigma_2^2sigma_1^(-1)sigma_2^(-2) or sigma_1sigma_2^(-1)sigma_1sigma_2^(-2) and Jones polynomial ...

The doublestruck capital letter Z, Z, denotes the ring of integers ..., -2, -1, 0, 1, 2, .... The symbol derives from the German word Zahl, meaning "number" (Dummit and Foote ...

Define the nome by q=e^(-piK^'(k)/K(k))=e^(ipitau), (1) where K(k) is the complete elliptic integral of the first kind with modulus k, K^'(k)=K(sqrt(1-k^2)) is the ...

The set of terms of first-order logic (also known as first-order predicate calculus) is defined by the following rules: 1. A variable is a term. 2. If f is an n-place ...

Calculus I

An arithmetic progression, also known as an arithmetic sequence, is a sequence of n numbers {a_0+kd}_(k=0)^(n-1) such that the differences between successive terms is a ...

A transformation in which coordinates in two spaces are expressed rationally in terms of those in another.

Erdős proved that there exist at least one prime of the form 4k+1 and at least one prime of the form 4k+3 between n and 2n for all n>6.

The conditional probability of an event A assuming that B has occurred, denoted P(A|B), equals P(A|B)=(P(A intersection B))/(P(B)), (1) which can be proven directly using a ...

The absence of contradiction (i.e., the ability to prove that a statement and its negative are both true) in an Axiomatic system is known as consistency.