Any other point of intersection between C and Af will be called a tangent point.

* Any locally compact Hausdorff space can be turned into a compact space by adding a single point to it, by means of Alexandroff one-point compactification.

Any piece of DNA with the point centromere DNA sequence on it will typically form a centomere if present in the appropriate species.

Any delusion on this point leads to the greatest errors, misfortunes, and troubles, and to the slavery of the soul.

Any increase of the drain-to-source voltage will increase the distance from drain to the pinch-off point, increasing resistance due to the depletion region proportionally to the applied drain-to-source voltage.

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 ).

Any given procedure might be called at any point during a program's execution, including by other procedures or itself.

Any point on a ray starting from point with direction ( here is a unit vector ) can be written as

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 neighbourhood N of x contains a neighbourhood M of x such that N is a neighbourhood of each point of M.

Any military planner would know that to mount a massive invasion of Europe from England, Allied units had to be staged around the country, with those that would land first nearest to the invasion point.

Any substance can be placed on a section of the strip revealing its thermal behaviour at the temperature at that point.

Any point on the frontier curve is Pareto efficient.

Any object radiating sound, including a loudspeaker system, can be thought of as being composed of combinations of such simple point sources.

Any planetary sized body at Earth's point should have been visible by the NASA STEREO coronagraphs during the first half of 2007.

Any player ( or, in some variations, only the dealer ) may at any time announce " point of order ," ( could also be " Court of Law " or " Point of Information " or " Point of Interest " or " Pevis " or " Coffee Break ") which is a signal for all players to put down their cards, while discussion takes place.

Any instrument will reach a point where an increase in sample concentration will not result in an increase in the reported absorbance, because the detector is simply responding to the stray light.

Any traveller attempting to pass into the eastern regions of Middle-earth would have to cross the Anduin at some point along its long course ( unless one passed through the extreme north, risking a passage through the Grey Mountains ).

Any point of law may be referred in this manner.

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 balance the music maintained up to that point, however fragile, is lost and so, more than likely, is the listener.

Any elliptic curve in Edwards form has a point of order 4.

:* Any total order on X has exactly one equivalence class, X itself, because x ~ y for all x and y ;

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

Any commutative monoid is endowed with its algebraic preordering ≤, defined by x ≤ y if and only if there exists z such that x + z = y.

Any statement of the form " for any number x ..." that is true for the reals is also true for the hyperreals.

Any preordered set ( P, ≤) forms a small category, where the objects are the members of P, the morphisms are arrows pointing from x to y when x ≤ y.

Any monoid ( any algebraic structure with a single associative binary operation and an identity element ) forms a small category with a single object x.

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 polynomial written in standard form has a unique constant term, which can be considered a coefficient of x < sup > 0 </ sup >.

* Any array of any length can so be divided up into sections of size L ( x ).

Any of the 100 squares in the superimposed 10 x 10 grid can be accurately described using a digit from 0-9 ( with 0 0 being the bottom left square and 9 9 being the top right square ).

A weight on a Lie algebra g over a field F is a linear map λ: g → F with λ ( y )= 0 for all x, y in g. Any weight on a Lie algebra g vanishes on the derived algebra and hence descends to a weight on the abelian Lie algebra g /.

Any transformation of the plane leaving this pattern invariant can be decomposed into a translation, ( x, y ) → ( n + x, y ), optionally followed by a reflection in either the horizontal axis, ( x, y ) → ( x ,− y ), or the vertical axis, ( x, y ) → (− x, y ), provided that this axis is chosen through or midway between two dots, or a rotation by 180 °, ( x, y ) → (− x ,− y ) ( ditto ).

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

Any accelerating electric charge, and therefore any changing electric current, gives rise to an electromagnetic wave that propagates at very high speed outside the surface of the conductor.

Any second-countable space is separable: if is a countable base, choosing any gives a countable dense subset.

* Properly with a generic referent: " Any cow gives milk.

Any meromorphic function f gives rise to a divisor denoted ( f ) defined as

* Any Lie group gives a Lie groupoid with one object, and conversely.

* Any foliation gives a Lie groupoid.

* Any principal bundle with structure group G gives a groupoid, namely over M, where G acts on the pairs componentwise.

Any smooth function on a symplectic manifold gives rise, by definition, to a Hamiltonian vector field and the set of all such form a subalgebra of the Lie Algebra of symplectic vector fields.

Any ξ ∈ gives rise to a canonical vertical vector field X < sub > ξ </ sub > by taking the derivative of the right action of the 1-parameter subgroup of H associated to ξ.

Any prime number p gives rise to an ideal pO < sub > K </ sub > in the ring of integers O < sub > K </ sub > of a quadratic field K.

Any n-dimensional formal group law gives an n dimensional Lie algebra over the ring R, defined in terms of the quadratic part F < sub > 2 </ sub > of the formal group law.

Any surface that intersects the wire has current I passing through it so Ampère's law gives the correct magnetic field.

Any ring homomorphism A → B gives a map K < sub > 0 </ sub >( A ) → K < sub > 0 </ sub >( B ) by mapping ( the class of ) a projective A-module M to M ⊗< sub > A </ sub > B, making K < sub > 0 </ sub > a covariant functor.

:( 1 ) Any person who manufactures, sells or hires or offers for sale or hire, or exposes or has in his possession for the purpose of sale or hire or lends or gives to any other person —

Any kind of connection on a manifold gives rise, through its parallel transport maps, to some notion of holonomy.

Any skew semistandard tableau of shape / with positive integer entries gives rise to a sequence of partitions ( or Young diagrams ), by starting with, and taking for the partition places further in the sequence the one whose diagram is obtained from that of by adding all the boxes that contain a value ≤ in ; this partition eventually becomes equal to.

Any attempt to drastically increase this range ( by increasing the angular extent of the true radius lobe nose region ) soon gives rise to problems with excessive rates of valve acceleration etc.

Any nontrivial line arrangement on RP < sup > 2 </ sup > defines a graph in which each face is bounded by at least three edges, and each edge bounds two faces ; so, double counting gives the additional inequality F ≤ 2E / 3.

Let now v and w be two vertices in G. Any spanning tree contains precisely one simple path between v and w. Taking this path in the uniform spanning tree gives a random simple path.

Any symmetric space gives an involutory quandle, where is the result of ' reflecting through '.

Any topological space X gives rise to a category where the objects are the points of X and the morphisms are the homotopy classes of paths.

In his letter, Polding gives Wardell a completely free hand in the design, saying " Any plan, any style, anything that is beautiful and grand, to the extent of our power.

Any premetric gives rise to a preclosure operator cl as follows: