what is infinity?

Answer 1

Infinity
The terms infinity and infinite have a variety of related meanings in mathematics. The adjective finite means “having an end,” so infinity may be used to refer to something having no end. In order to give a precise definition, the mathematical domain of discoursemust be specified.

Set theory provides a simple and basic example of an infinite collection—the class of natural numbers, or positive integers. A fundamental property of positive integers is that after each integer there follows a next one, so that there is no last integer. Now it is necessary in mathematics to treat the collection of all positive integers as an entity, and this entity is the simplest infinity, or infinite collection.

The term infinity appears in mathematics in a different sense in connection with limits of functions. For example, consider the function defined by y = 1/x. When x tends to 0, y approaches infinity, and the expression may be written as shown below.

Precisely, this means that for an arbitrary number a > 0, there exists a number b > 0 such that when 0 < x < b, then y > a, and when ?b < x < 0, then y < ?a. This example indicates that it is sometimes useful to distinguish +? and ??. The points +? and ?? are pictured at the two ends of the y axis, a line which has no ends in the proper sense of euclidean geometry.

In geometry of two or more dimensions, it is sometimes said that two parallel lines meet at infinity. This leads to the conception of just one point at infinity on each set of parallel lines and of a line at infinity on each set of parallel planes. With such agreements, parts of euclidean geometry can be discussed in the terms of projective geometry. For example, one may speak of the asymptotes of a hyperbola as being tangent to the hyperbola at infinity.

Answer 2

Infinity-

1. limitless time, space, or distance
beyond the Earth lay infinity

2. an amount or number so great that it cannot be counted
an infinity of stars

3. the state or quality of being infinite
4. the concept of being unlimited by always being larger than any imposed value or boundary. For some purposes this may be considered as being the same as one divided by zero.
5. a part of a geometric figure situated an infinite distance from the observer, for example the hypothetical point at which parallel lines meet in Euclidean geometry
6. a point sufficiently far from a lens or mirror that the light emitted from it falls in parallel rays on the surface

Answer 3

the concept of something that is unlimited, endless, without bound. The common symbol for infinity was invented by the English mathematician John Wallis in 1657. Three main types of infinity may be distinguished: the mathematical, the physical, and the metaphysical. Mathematical infinities occur, for instance, as the number of points on a continuous line or as the size of the endless sequence of counting numbers: 1, 2, 3,…. Spatial and temporal concepts of infinity occur in physics when one asks if there are infinitely many stars or if the universe will last forever. In a metaphysical discussion of God or the Absolute, there are questions of whether an ultimate entity must be infinite and whether lesser things could be infinite as well.

Answer 4

Infinity

The terms infinity and infinite have a variety of related meanings in mathematics. The adjective finite means “having an end,” so infinity may be used to refer to something having no end. In order to give a precise definition, the mathematical domain of discoursemust be specified.

Set theory provides a simple and basic example of an infinite collection—the class of natural numbers, or positive integers. A fundamental property of positive integers is that after each integer there follows a next one, so that there is no last integer. Now it is necessary in mathematics to treat the collection of all positive integers as an entity, and this entity is the simplest infinity, or infinite collection.

The term infinity appears in mathematics in a different sense in connection with limits of functions. For example, consider the function defined by y = 1/x. When x tends to 0, y approaches infinity, and the expression may be written as shown below. \lim_{x\to 0}y=\infty

Precisely, this means that for an arbitrary number a > 0, there exists a number b > 0 such that when 0 < x < b, then y > a, and when ?b < x < 0, then y < ?a. This example indicates that it is sometimes useful to distinguish +? and ??. The points +? and ?? are pictured at the two ends of the y axis, a line which has no ends in the proper sense of euclidean geometry.

In geometry of two or more dimensions, it is sometimes said that two parallel lines meet at infinity. This leads to the conception of just one point at infinity on each set of parallel lines and of a line at infinity on each set of parallel planes. With such agreements, parts of euclidean geometry can be discussed in the terms of projective geometry. For example, one may speak of the asymptotes of a hyperbola as being tangent to the hyperbola at infinity.

Answer 5

Infinity is the concept of being neverendingly great; it isn't a number like some would be under the misconception of noting (ex: I'm better than you times INFINITY!!" lol)

It is simply the state in which there is no limit to an entity's largeness, OR going in the opposite direction, an entity's smallness ("infinitesimal" being one branch off the meaning "infinite" which means "indefinately or exceedingly small.")

Basically, infinity refers to some quantity of which its value grows but without fail, goes into the unknown. When speaking of such quantities, it does well to see THE WAY by which a value continues without end rather than just the mere fact that it does continue in that manner. When something is known to be infinite, the trend at which it goes about being infinite is more interesting to observe.

Hope this answers your question...

Answer 6

Infinity can not be sped up in the way you're wondering. that's the cost in basic terms previous the decision line, as such, there is no longer a discrete degree. although, there are diverse "kinds" of infinity, there will be more desirable and lesser quantities of infinity. evaluate the set of complicated numbers, the position i is the sq. root of adverse one. so that they kind a set of numbers a+bi in the time of a plane with the genuine line being one axis and the imaginary line being the different axis. Now evaluate the set of organic numbers, they're a subset of the genuine line and at the same time as the genuine line is uncountable, the organic set is countable. in view that section is the geometric results of multiplication, extra precisely rectangles, then in case you're taking the genuine line at properly angles you ultimately end up with a real plane, the x-y plane. it truly is likewise infinity and ought to nicely be what you're searching for, or again utilising extra appropriate kind, the complicated plane with the i conjugate on the y axis. I fairly have a extra appropriate one for you to contemplate. imagine a real decision, say call it d, that's close to to 0, yet no longer 0. more desirable, enable us imagine it truly is a small effective decision, more desirable imagine a decision that once coming from the right is continuously to the left of you, yet continuously to the right of 0. This decision should be infinitely small. Now that's an beautiful decision.

Answer 7

In mathematics, there are more than one infinities.

The one you are used to is the number of integers. Start with 1, and keep adding 1. 1,2,3,4,5, and so on. Infinity is the number of all those numbers.

Take a piece of paper that's infinity inches long and infinity inches wide. Draw a curved or straight line on it. Keep doing that for every possible line on that piece of paper. That's another infinity, which is bigger than the first one.

Infinity is something that stretches your mind.

Answer 8

all very nice answers, some quite high-brow stuff for a simple question.

Check the dictionary for the definition.
For a practical exercise try this:-

1) start with the largest number you can reasonably think of.
2) add 1 to that number
3) repeat step 2 until you grow old and die
4) instruct any descendants you may have (sons, daughters) to continue with this test. Tell them to pass on these instructions to their kids, and so on and so on.

When the universe collapses or we all kill each other in some kind of armageddon, the number which your last living descendant has reached will be no closer to infinity than when you started.

Hope that helps!

Answer 9

I think the best definition of infinity is that provided in the "Hitchhikers Guide to the Galaxy" by Douglas Adams:

"Bigger than the biggest thing ever and then some. Much bigger than that in fact, really amazingly immense, a totally stunning size, real "wow, that's big," time. Infinity is just so big that by comparison, bigness itself looks really titchy. Gigantic multiplied by staggeringly huge is the sort of concept we're trying to get across here."

Answer 10

I like to think of infinity as a label for an 'unknown' number.

A pure maths professor once told me . . .
"Imagine a hotel with an infinite number of rooms - infinity is the room with INFINITY labelled on the door"!

This analogy helps me put a label on infinity - otherwise it is a ever increasing number that could blow your mind if you thought about it too much!

For a fascinating account of Infinity please see ref below.