* Any field, including fields of rational numbers, real numbers, and complex numbers.

Any non-trivial true statement about reality is necessarily an abstraction composed of a complex of objects and properties or relations.

* Any polynomial ( real or complex ) is an analytic function.

Any Taylor series for this function converges not only for x close enough to x < sub > 0 </ sub > ( as in the definition ) but for all values of x ( real or complex ).

Any real analytic function on some open set on the real line can be extended to a complex analytic function on some open set of the complex plane.

Any quadratic polynomial over the complex numbers ( polynomials of the form where,, and ∈ ) can be factored into an expression with the form using the quadratic formula.

* Any open subset of a finite-dimensional real, and therefore complex, vector space is a diffeological space.

* Any narrow complex tachycardia combined with a problem with the conduction system of the heart, often termed " supraventricular tachycardia with aberrancy.

To show that U ( n ) is connected, recall that any unitary matrix A can be diagonalized by another unitary matrix S. Any diagonal unitary matrix must have complex numbers of absolute value 1 on the main diagonal.

Any number system that forms a commutative ring — for instance, the integers, the real numbers, and the complex numbers — can be extended to a wheel in which division by zero is always possible ; however, in such a case, " division " has a slightly different meaning.

Any complex number may be written a + bi, where a and b are real numbers and i is the imaginary unit.

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 new system of romanization, regardless of its merits, makes romanization choices more complex rather than more simple.

Any product where one material slides or rubs over another is affected by complex tribological interactions, whether lubricated like hip implants and other artificial prostheses, or unlubricated as in high temperature sliding wear in which conventional lubricants cannot be used but in which the formation of compacted oxide layer glazes have been observed to protect against wear.

Any of these conditions implies the existence of a unique compatible complex structure.

Through an evaluation and bidding process, the Apple II was chosen by MECC for state schools over other candidates, such as the Radio Shack TRS-80 ; the win was an important early deal in the history of Apple Inc. Any school in the state could buy Apple computers through MECC for a substantial discount without having to go through complex evaluation and purchasing procedures.

Any “ nice ” space such as a manifold or CW complex is semi-locally simply connected.

Any such complex torus has the Gaussian integers as endomorphism ring.

Any conception of a traditional market for making beneficial exchanges, such as an agricultural market or trading pit, or any system where individuals respond to posted prices on a computer screen is woefully inadequate for the extremely large number of often complex trades that will be required.

Any tool that tries to simplify a complex picture will introduce distortions, whether it is a geographic map or a set of scenarios.

Any investment in a war would be expected to bring a return of plunder and prisoners, which became part of the endowment of the palace complex.

Any basis for V over the real numbers serves as a basis for V < sup > C </ sup > over the complex numbers.

Any continuous periodic function can be represented as a complex harmonic motion using its fourier series.

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

# 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 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 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 finite number of initial terms of the Taylor series of a function is called a Taylor polynomial.

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.