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A theory is a set of sentences which is closed under logical implication. That is, given any subset of sentences {s_1,s_2,...} in the theory, if sentence r is a logical ...

Let rho be a reciprocal difference. Then Thiele's interpolation formula is the continued fraction f(x)=f(x_1)+(x-x_1)/(rho(x_1,x_2)+)(x-x_2)/(rho_2(x_1,x_2,x_3)-f(x_1)+) ...

A lamp is turned on for 1/2 minute, off for 1/4 minute, on for 1/8 minute, etc. At the end of one minute, the lamp switch will have been moved aleph_0 times, where aleph_0 is ...

The larger an arc is, the smaller its radius appears. For example, the three arcs illustrated above belong circles of the same radius.

A self-avoiding walk in which steps may be to the left, right, or straight ahead after a vertical step, but only straight ahead or to the left after a horizontal step. A ...

A three-colorable graph G is a graph with chromatic number chi(G)<=3.

A logical structure which does not assume the law of the excluded middle. Three truth values are possible: true, false, or undecided. There are 3072 such logics.

A strategy for the iterated prisoner's dilemma in which a prisoner cooperates on the first move, and thereafter copies the previous move of the other prisoner. Any better ...

The quartic surface given by the equation x^4+y^4+z^4-(x^2+y^2+z^2)=0.

A simple unlabeled graph whose connectivity is considered purely on the basis of topological equivalence, so that two edges (v_1,v_2) and (v_2,v_3) joined by a node v_2 of ...