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A partial differential equation (PDE) is an equation involving functions and their partial derivatives; for example, the wave equation ...

The nth partial numerator in a generalized continued fraction b_0+K_(n=1)^infty(a_n)/(b_n) is the expression a_n. For a simple continued fraction b_0+K_(n=1)^infty1/(b_n), ...

An ideal I of a partial order P is a subset of the elements of P which satisfy the property that if y in I and x<y, then x in I. For k disjoint chains in which the ith chain ...

For a partial order, the size of the longest chain is called the length.

For a partial order, the size of the longest antichain is called the width.

Given a sequence {a_k}_(k=1)^n, a partial sum of the first N terms is given by S_N=sum_(k=1)^Na_k.

Each subsequent row of Pascal's triangle is obtained by adding the two entries diagonally above. This follows immediately from the binomial coefficient identity (n; r) = ...

"God is or He is not...Let us weigh the gain and the loss in choosing...'God is.' If you gain, you gain all, if you lose, you lose nothing. Wager, then, unhesitatingly, that ...

The Pasch configuration is the unbalanced (6_2,4_3) configuration (since there are two lines through each of six points and three points on each of four lines) illustrated ...

In the plane, if a line intersects one side of a triangle and misses the three vertices, then it must intersect one of the other two sides. This is a special case of the ...