Thus intuitionists absolutely disallow the blanket assertion: " For all propositions P concerning infinite sets D: P or ~ P " ( Kleene 1952: 48 ).

: For more about the conflict between the intuitionists ( e. g. Brouwer ) and the formalists ( Hilbert ) see Foundations of mathematics and Intuitionism.

For example: in the First Antinomy, Kant proves the thesis that time must have a beginning by showing that if time had no beginning, then an infinity would have elapsed up until the present moment.

For any topological space X the ( Alexandroff ) one-point compactification αX of X is obtained by adding one extra point ∞ ( often called a point at infinity ) and defining the open sets of the new space to be the open sets of X together with the sets of the form G < font face =" Arial, Helvetica "> U </ font >

For exponents equal to positive or negative infinity the means are maximum and minimum, respectively, regardless of weights ( and they are actually the limit points for exponents approaching the respective extremes ):

Highly enriched uranium ( HEU ) has a greater than 20 % concentration of < sup > 235 </ sup > U or < sup > 233 </ sup > U. The fissile uranium in nuclear weapons usually contains 85 % or more of < sup > 235 </ sup > U known as weapon ( s )- grade, though for a crude, inefficient weapon 20 % is sufficient ( called weapon ( s )- usable ); in theory even lower enrichment is sufficient, but then the critical mass for unmoderated fast neutrons rapidly increases, approaching infinity at 6 % < sup > 235 </ sup > U. For criticality experiments, enrichment of uranium to over 97 % has been accomplished.

For example, stereographic projection of a sphere onto the plane augmented with a point at infinity is a conformal map.

For instance, in the ferromagnetic transition, the heat capacity diverges to infinity.

For example, according to Fourier equation, a pulse of heat at the origin would be felt at infinity instantaneously.

For example, the Hebrew letter aleph (" א ") is often used by mathematicians to denote certain kinds of infinity, but it is also used in ordinary Hebrew text.

For a pole of the function f ( z ) at point a the function approaches infinity as z approaches a.

For example, the quantum finite automaton or topological automaton has uncountable infinity of states.

* For any consistent theory this usually does not give just one world of objects, but an infinity of possible worlds that the theory might equally describe, with a possible diversity of truths between them.

For example, a naive quantum mechanical calculation of the ground-state energy density yields infinity, which is unreasonable.

According to Aristotle, a future span of time must be a potential infinity, because another element can always be added to a series that is inexhaustible: " For generally the infinite has this mode of existence: one thing is always being taken after another, and each thing that is taken is always finite, but always different ".

For example, parallel and nonparallel lines need not be treated as separate cases – we single out some arbitrary projective plane as the ideal plane and locate it " at infinity " using homogeneous coordinates.

For a beam focused at infinity, the far-field region is sometimes referred to as the " Fraunhofer region ".

For instance, Möbius transformations ( transformations of the complex projective line, or Riemann sphere ) are affine ( transformations of the complex plane ) if and only if they fix the point at infinity.

For some probabilistic source models, the best performance may be achieved when approaches infinity.

For any locally compact Hausdorff topological space X, the space C < sub > 0 </ sub >( X ) of continuous complex-valued functions on X which vanish at infinity is in a natural way a commutative C *- algebra:

For the step function, the magnitude of the undershoot is thus exactly the integral of the ( left ) tail, integrating to the first negative zero: for the normalized sinc of unit sampling period, this is The overshoot is accordingly of the same magnitude: the integral of the right tail, or, which amounts to the same thing, the difference between the integral from negative infinity to the first positive zero, minus 1 ( the non-overshooting value ).

For example, the pencil of curves ( 1-dimensional linear system of conics ) defined by is non-degenerate for but is degenerate for concretely, it is an ellipse for two parallel lines for and a hyperbola with < math > a < 0 </ math > – throughout, one axis has length 2 and the other has length which is infinity for

For non-constant meromorphic functions in the plane, T ( r, f ) tends to infinity as r tends to infinity,

For instance, by using homogeneous coordinates, the w-coordinate may be set to zero to extend a point to infinity.

For any summation method L, its abelian theorem is the result that if c = ( c < sub > n </ sub >) is a convergent sequence, with limit C, then L ( c ) = C. An example is given by the Cesàro method, in which L is defined as the limit of the arithmetic means of the first N terms of c, as N tends to infinity.

For one thing, this is not a subject often discussed or analyzed.

For better or for worse, we all now live in welfare states, the organizing principle of which is collective responsibility for individual well-being.

For one thing, there is a natural belt of rock across the river bed ; ;

For the family is the simplest example of just such a unit, composed of people, which gives us both some immunity from, and a way of dealing with, other people.

Even so astute a commentator as Harold Clurman of The Nation has said that `` Waiting For Godot '' is `` the concentrate of the contemporary European mood of despair ''.

For one thing, the world that Beckett sees is already shattered.

Harold Clurman is right to say that `` Waiting For Godot '' is a reflection ( he calls it a distorted reflection ) `` of the impasse and disarray of Europe's present politics, ethic, and common way of life ''.

For the beatnik, like the hipster, is in opposition to a society that is based on the repression of the sex instinct.

For this reason, too, their language is more forthright and earthy.

For the present it is enough to note that in the grotesque figure of Jacoby, at the moment of his collapse, all these elements come together in prophetic parody.

For Plato, `` imitation '' is twice removed from reality, being a poor copy of physical appearance, which in itself is a poor copy of ideal essence.

For both Plato and Aristotle artistic mimesis, in contrast to the power of dialectic, is relatively incapable of expressing the character of fundamental reality.

For Hammer, nothing is forbidden.

For example, suppose a man wearing a $200 watch, driving a 1959 Rolls Royce, stops to ask a man on the sidewalk, `` What time is it ''??

For the occasion on which everyone already knows everyone else and the host wishes them to meet one or a few honored newcomers, then the `` open house '' system is advantageous because the honored guests are fixed connective points and the drifting guests make and break connections at the door.

For this change is not a change from one positive position to another, but a change from order and truth to disorder and negation.

For paradigmatic history `` breaks '' rather than unfolds precisely when the movement is from order to disorder, and not from one order to a new order.

For this love of the boy for his mother is a hopeless and forbidden love, doomed by its nature.

For innocence, of all the graces of the spirit, is I believe the one most to be prayed for.

For what we propose, however, a psychoanalyst is not necessary, even though one aim is to enable the reader to get beneath his own defenses -- his defenses of himself to himself.

For this purpose a degree of intellectual and emotional involvement is necessary ; ;