Word Finder - infinity

definition

Endlessness, unlimitedness, absence of a beginning, end or limits to size.

definition

A number that has an infinite numerical value that cannot be counted.

definition

An idealised point which is said to be approached by sequences of values whose magnitudes increase without bound.

definition

A number which is very large compared to some characteristic number. For example, in optics, an object which is much further away than the focal length of a lens is said to be "at infinity", as the distance of the image from the lens varies very little as the distance increases further.

definition

The symbol ∞.

We have intuitions of cause, of infinity, of good and Flint.

The line la+ma+ny is the radical axis, and since as+43 c-y =o is the line infinity, it is obvious that equation (I) represents a conic passing through the circular points, i.e.

The process by which the mind is thus stored consists of an infinity of individual impressions.

If in a central orbit the velocity is equal to the velocity from infinity, we have, from (5),

If we now imagine the point 0 to recede to infinity, the forces P, Q and the resultant R are parallel, and we have R=P+Q, P.AC=Q.CB.

A band might in that case fade away towards zero frequencies, and as s increases, return again from infinity with diminishing distances, the head and the tail pointing in the same direction; or with a different value of constants a band might fade away towards infinite frequencies, then return through the whole range of the spectrum to zero frequencies, and once more return with its tail near its head.

God does not seem to find much place in the Wissenschaftslehre, where mankind is the absolute and nature mankind's product, and where God neither could be an absolute Ego which posits objects in the non-Ego to infinity without ever completing the process, nor could be even known to exist apart from the moral order which is man's destination.

Thus his pantheistic is also a teleological idealism, which in its emphasis on free activity and moral order recalls Leibnitz and Fichte, but in its emphasis on the infinity of God has more affinity to Spinoza, Schelling and Hegel.

He accepts an ultimate antinomy as to the finiteness or infinity of " the unconditioned," yet applies the law of the excluded middle to insist that one of the two alternatives must be true, wherefore we must make the choice.

But ecclesiastical politics gave him an infinity of trouble.

In these tribes the bold and active habits, the striking colours, or the fantastic diversities of structure,have so long attracted remark that recent investigations, while adding a multitude of new species and supplying the specialist with an infinity of new details, have not materially altered the scientific standpoint.

On submitting a complex substance of this character to destructive distillation, it will be found that the yield and quality of the products will vary very considerably with the temperature existing in the retorts, with the size of the charge of coal used, with its distribution in the retort, with the length of time the distillation has been going on, and with an infinity of other factors of a more or less complex nature.

These have now to pass down the heated retort on their way to the ascension pipe, and the contact with the heated sides of the retort, and the baking from the radiant heat in the retort, set up an infinity of changes.

The entrance window is then the real image of this diaphragm projected by the objective in the surface conjugate to the plane focused for, and the exit window is the image projected by the eyepiece; this happens with the image of the object lying at infinity.

Hiroshima, visited by a bomb of exponential power, reached an infinity of destruction in seconds.

While the Tao symbol is probably better known as the yin yang symbol, the encircled symbol represents the never-ending energy of chi, which is the concept of infinity.

Take caution, though, a wide band infinity ring may overshadow a simpler engagement ring.

Diamond infinity rings are beautiful designs as rich with symbolism as they are with precious stones and sparkle.

The new Angels Infinity Edge Demi is available online and in stores now.

Taking this ideal limit as a theoretical or absolute zero, the value of H may be represented on the diagram by the whole area included between the two adiabatics BAZ, CDZ' down to the points where they intersect the isothermal of absolute zero, or the zero isopiestic OV asymptotically at infinity.

The term "Nature" is put more into the foreground in the Treatise, a point which might be urged as evidence of Bruno's influence - the dialogues, moreover, being specially concerned to establish the unity, infinity and selfcontainedness of Nature 2; but the two opposed Cartesian attributes, thought and extension, and the absolutely infinite substance whose attributes they are - substance constituted by infinite attributes - appear here as in the Ethics.

At first the tension will diminish, but if the process be continued the tension will reach a minimum value and will afterwards increase to infinity as the chain between A and B approaches to the form of a straight line.

Thus mathematics assumes space as an existent infinite, without investigating in what sense the existence or the infinity of this Unding, as Kant called it, can be asserted.

The frank recognition that local income taxes are impossible, and that taxation on property for local purposes can only be applied to real property, where it becomes, usually or frequently, in the nature of a rent-charge, would have saved the legislature and the public an infinity of laborious discussion.

The sun is a small target for a meteorite coming from infinity to hit, and if this considerable quantity reaches its mark, a much greater amount will circulate round the sun in parabolas, and there is no evidence of it where it would certainly make itself felt, in perturbations of the planets.

Beyond mention, there is little to be said, owing to the absence of general principles in an infinity of specific details, mostly domestic and apparently trivial.

We have, in the case just referred to, to take account of a point at infinity on the line y=0; the two intersections are the point (x=110, y=0), and the point at infinity on the line y= 0.

It is, moreover, to be noticed that the points at infinity may be all or any of them imaginary, and that the points of intersection, whether finite or at infinity, real or imaginary, may coincide two or more of them together, and have to be counted accordingly; to support the theorem in its universality, it is necessary to take account of these various circumstances.

Say the projection is always a line, then if the figure is such that the two planes are parallel, the projection is the intersection of the given plane by a parallel plane, or it is the system of points at infinity on the given plane, that is, these points at infinity are regarded as situate on a given line, the line infinity of the given plane.

Reverting to the purely plane theory, infinity is a line, related like any other right line to the curve, and thus intersecting it in m points, real or imaginary, distinct or coincident.

The points in question have since been called (it is believed first by Dr George Salmon) the circular points at infinity, or they may be called the circular points; these are also frequently spoken of as the points I, J; and we have thus the circle characterized as a conic which passes through the two circular points at infinity; the number of conditions thus imposed upon the conic is = 2, and there remain three arbitrary constants, which is the right number for the circle.

Poncelet throughout his work makes continual use of the foregoing theories of imaginaries and infinity, and also of the before-mentioned theory of reciprocal polars.

Names may also be used for the different forms of infinite branches, but we have first to consider the distinction of hyperbolic and parabolic. The leg of an infinite branch may have at the extremity a tangent; this is an asymptote of the curve, and the leg is then hyperbolic; or the leg may tend to a fixed direction, but so that the tangent goes further and further off to infinity, and the leg is then parabolic; a branch may thus be hyperbolic or parabolic as to its two legs; or it may be hyperbolic as to one leg and parabolic as to the other.

If a line S2 cut an arc aa at b, so that the two segments ab, ba lie on opposite sides of the line, then projecting the figure so that the line Sl goes off to infinity, the tangent at b is projected into the asymptote, and the arc ab is projected into a hyperbolic leg touching the asymptote at one extremity; the arc ba will at the same time be projected into a hyperbolic leg touching the same asymptote at the other extremity (and on the opposite side), but so that the two hyperbolic legs may or may not belong to one and the same branch.

And we thus see that the two hyperbolic legs belong to a simple intersection of the curve by the line infinity.

The foregoing considerations also show (what is very important) how different branches are connected together at infinity, and lead to the notion of a complete branch or circuit.

First, if the three intersections by the line infinity are all distinct, we have the hyperbolas; if the points are real, the redundant hyperbolas, with three hyperbolic branches; but if only one of them is real, the defective hyperbolas, with one hyperbolic branch.

But although we thus arrive by projection at the notion of a circuit, it is not necessary to go out of the plane, and we may (with Zeuthen, using the shorter term circuit for his complete branch) define a circuit as any portion (of a curve) capable of description by the continuous motion of a point, it being understood that a passage through infinity is permitted.

This is Spinoza's theory of the infinitely infinite," the limiting notion of infinity being of a numerical, quantitative series, each term of which is a qualitative determination itself quantitatively little, e.g.

The doctrine of geometrical continuity and the application of algebra to geometry, developed in the 16th and 17th centuries mainly by Kepler and Descartes, led to the discovery of many properties which gave to the notion of infinity, as a localized space conception, a predominant importance.

A line became continuous, returning into itself by way of infinity; two parallel lines intersect in a point at infinity; all circles pass through two fixed points at infinity (the circular points); two spheres intersect in a fixed circle at infinity; an asymptote became a tangent at infinity; the foci of a conic became the intersections of the tangents from the circular points at infinity; the centre of a conic the pole of the line at infinity, &c. In analytical geometry the line at infinity plays an important part in trilinear co-ordinates.

The infinity of real existence, in contrast with the necessary finitude of human understanding and experience, is always in his thoughts.

To prove this, our thoughts of space, time, infinity, power, substance, personal identity, causality, and others which " seem most remote from the supposed original " are examined in a " plain historical method," and shown to depend either on (a) perception of things external, through the five senses, or on (b) reflection upon operations of the mind within.

If one of the foci be at infinity, the conics are confocal parabolas, which may also be regarded as parabolas having a common focus and axis.

The eyepiece, which by means of narrow pencils represents the relatively large real image at infinity, transmits from all points of this real image parallel pencils, whereby the inclination of the principal rays becomes further increased.

Its purpose in a microscope is by means of narrow cones of rays to represent at infinity the real magnified image which the objective produces.

It will satisfy Infinity and Choice if the original model of TST satisfies these axioms.

In fact, the infinity fryer has been scientifically proven to produce food with up to 25% less fat.

His first novel, To hold infinity, was one of the Daily Telegraph's ' Books of the Year ' .

It reaches the minimum in a circular object and approaches infinity in thin, complex objects.