* Any finite topological space, including the empty set, is compact.

# Any collection of closed subsets of X with the finite intersection property has nonempty intersection.

Any rational number with a denominator whose only prime factors are 2 and / or 5 may be precisely expressed as a decimal fraction and has a finite decimal expansion.

* Any two finite fields with the same number of elements are isomorphic.

# Any finite straight line can be extended in a straight line.

* Any simply connected solvable Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

* Any simply connected nilpotent Lie group is isomorphic to a closed subgroup of the group of invertible upper triangular matrices with 1's on the diagonal of some rank, and any finite dimensional irreducible representation of such a group is 1 dimensional.

Any meaningful theory of quantum gravity that makes sense and is predictive at all energy scales must have some deep principle that reduces the infinitely many unknown parameters to a finite number that can then be measured.

Any topological space which is itself finite or countably infinite is separable, for the whole space is a countable dense subset of itself.

Any symmetry group whose elements have a common fixed point, which is true for all finite symmetry groups and also for the symmetry groups of bounded figures, can be represented as a subgroup of orthogonal group O ( n ) by choosing the origin to be a fixed point.

Any digital modulation scheme uses a finite number of distinct signals to represent digital data.

Any finite product in a preadditive category must also be a coproduct, and conversely.

Any finite subcover of this cover must be bounded, because all balls in the subcover are contained in the largest open ball within that subcover.

According to the historian of science Norwood Russell Hanson: There is no bilaterally-symmetrical, nor excentrically-periodic curve used in any branch of astrophysics or observational astronomy which could not be smoothly plotted as the resultant motion of a point turning within a constellation of epicycles, finite in number, revolving around a fixed deferent. Any path — periodic or not, closed or open — can be represented with an infinite number of epicycles.

Any rational function of a real variable can be written as the sum of a polynomial function and a finite number of algebraic fractions.

* Any finite contiguous subsequence of a word

Any finite extension of a finite field is a cyclic extension.

Any structure implicit in the finite entropy against a quantum description could then be totally washed out by the huge injection of uncertainty this projection represents.

Any Calabi – Yau manifold has a finite cover that is the product of a torus and a simply-connected Calabi – Yau manifold.

Any finite simplicial complex in the sense talked about here can be embedded as a polytope in that sense, in some large number of dimensions.

Any Fredholm operator has an index, defined as the difference between the ( finite ) dimension of the kernel of D ( solutions of Df = 0 ), and the ( finite ) dimension of the cokernel of D ( the constraints on the right-hand-side of an inhomogeneous equation like Df

* Any category with finite products is monoidal with the product as the monoidal product and the terminal object as the unit.

Any number of other ways exist to be rich.

* Any expression formed using any combination of the basic arithmetic operations and extraction of nth roots gives an algebraic number.

Any number of players may be replaced by substitutes during the course of the game.

Any season ticket holder could put themselves forward for election, with a certain number of nominations, and votes were cast by all season ticket holders over the age of 18.

# Any real number can be added to both sides.

# Any real number can be subtracted from both sides.

# Any real number can be multiplied to both sides.

# Any non-zero real number can divide both sides.

Any complex number z = x + iy can be written as

# Any player who would qualify from the Interzonal to play in the Candidates but who was excluded because of a limitation on the number of participants from his Federation.

* Any of a number of plants in the family Poaceae with narrow blade-shaped leaves, or other unrelated plants of similar appearance

Any decision involves a choice selected from a number of alternatives, directed toward an organizational goal or subgoal.

Any number of these monomer units may be indicated by the appropriate Greek prefix ; e. g. a decamer is formed from 10 monomers.

Any overbid or underbid loses the number of points their bid was off ( a player bidding 3 tricks that wins only 2 would lose a point, as would a player bidding 2 and winning 3 ).

Simple Plan, from Montréal, climbed to number three in the United States with Still Not Getting Any ... in 2004.

Any number of players can play, using differently coloured pens, if required.

* Any topological space which is the union of a countable number of separable subspaces is separable.

Any number of other alternate forms may be used, many of which are variations on the term " gamemaster "; these variants are especially common in storytelling games derived from or similar to role-playing games.

Any Liouville number must have unbounded partial quotients in its continued fraction expansion.

Any modulated signal will have an infinite number of sidebands and hence an infinite bandwidth but in practice all significant sideband energy ( 98 % or more ) is concentrated within the bandwidth defined by Carson's rule.

Any type or number of topologies may be used -- star, bus, ring, etc.