Definitions
from The American Heritage® Dictionary of the English Language, 4th Edition
 n. The quality or condition of being infinite.
 n. Unbounded space, time, or quantity.
 n. An indefinitely large number or amount.
 n. Mathematics The limit that a function ∫ is said to approach at x = a when ∫(x) is larger than any preassigned number for all x sufficiently near a.
 n. A range in relation to an optical system, such as a camera lens, representing distances great enough that light rays reflected from objects within the range may be regarded as parallel.
 n. A distance setting, as on a camera, beyond which the entire field is in focus.
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. Limitlessness, unlimitedness, something which is growing without limits or bounds.
 n. A number that has an infinite numerical value that cannot be counted.
 n. 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.
 n. The symbol ∞.
from the GNU version of the Collaborative International Dictionary of English
 n. Unlimited extent of time, space, or quantity; eternity; boundlessness; immensity.
 n. Unlimited capacity, energy, excellence, or knowledge.
 n. Endless or indefinite number; great multitude; as an infinity of beauties.
 n. A quantity greater than any assignable quantity of the same kind.
 n. That part of a line, or of a plane, or of space, which is infinitely distant. In modern geometry, parallel lines or planes are sometimes treated as lines or planes meeting at infinity.
from The Century Dictionary and Cyclopedia
 n. The condition of being infinite or the greatest possible; immeasurableness; innumerability; perfection: as, the infinity of God; infinity of duration.
 n. Unlimited extension; figuratively, exhaustless quantity or number: as, inconceivable infinity; an infinity of details.
 n. In geometry, the part of space at an infinite distance from the part chiefly considered.
 n. An infinite number: as, an infinity of straight lines. Its symbol is ∞.
from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.
 n. time without end
Etymologies
from Wiktionary, Creative Commons Attribution/ShareAlike License
Examples

So what I’m wondering is, does this mean that from the point of view of Schwarzschild coordinates, the object is behaving like a white hole from Schwarzschild time  infinity to 0, and then behaving like a black hole from Schwarzschild time 0 to +infinity?

Like the concepts of quantity, limit, boundary, the term infinity applies primarily to space and time, but not exclusively, as

While Dad hid in the back of the house all night, I laid awake on the living room couch next to the hospital bed, like summers when I was a kid and used to float on my back in the pool, trying to make sense of stars, and the uneasy feeling I got from the word infinity.

Now, with Bernie Madoff, what happened was what you call infinity scam.

In mathematics there is what we called infinity and "Design = Infinity".

The idea of summing all costs from here to infinity is preposterous, because we simply cannot know what the future will bring.
The Volokh Conspiracy » Would the Public Support “Cap and Refund”?

Its limit as time approaches infinity is sclerotic Brezhnevism.

All the different stories and opinions gathered together here glance off of one another like a hall of mirrors, but the figure reflected into infinity is that of the woman who continues to define herself more through her relationships than through her work.

What gets me about infinity is this: when one states that time or space might not be infinite, I wonder what is to the left of the end of space, or what happened one second before time began?

The nature of infinity is this: That every thing has its
'If the acts have been perform'd let the Bard himself witness': William Blake's Milton and MOO space
fbharjo commented on the word infinity
...omega cone's skin...
January 26, 2013
bilby commented on the word infinity
"...an imaginary nodal circle.."
January 26, 2013
marky commented on the word infinity
the brink of existence.
November 21, 2010
oroboros commented on the word infinity
You're Infinity's
Local Representative.
Doesn't that feel great?
Stu Charno
December 13, 2007
oroboros commented on the word infinity
See: Poetrie: Infinity
March 13, 2007