infinity
Pluralinfinities (some meanings)
- 1The state or quality of being endless and unlimited, with no beginning, no end, and no limit to size.
Philosophers have long argued over whether the universe extends to infinity or ends somewhere.
Her novel tries to convey the infinity of time, which has no first moment and no last.
Similarendlessness, boundlessness, limitlessness, infinitude
Oppositefiniteness
Note
This is the root sense, and the Latin spells it out: īnfīnitās, "unlimitedness", from in- "not" and fīnis "end", with -tās turning the whole into a state. It reached English through Old French infinité. Used this way the word takes no plural: one speaks of the infinity of space or of time, and the plural infinities belongs to the mathematical value.
- 2In mathematics, a number with an infinite value, one that cannot be counted.
Physicists spent years learning to tame the infinities that appeared whenever they calculated the electron's self-energy.
Under standard floating-point rules, dividing a positive number by zero produces positive infinity.
Note
Mathematics places it outside the real numbers. Ordinary arithmetic does not hold for it, so the number system has to be extended to admit it. Physicists use the plural for values that run out of control: Michael Riordan's "Tackling Infinity" in American Scientist (2012) describes quantum electrodynamics and quantum gravity as dogged by infinities that erupt when calculations are pushed into new domains.
- 3The written sign ∞, shaped like a figure eight lying on its side.
In the formula, a small infinity sits above the summation sign.
The jeweler engraved an infinity between the couple's initials on the inside of the ring.
- 4In analysis and topology, an idealized point that sequences of values are said to approach when their magnitudes increase without bound.
As n tends to infinity, the partial sums of 1 + 1/2 + 1/4 + … approach 2.
In projective geometry, two parallel lines meet at a single point at infinity.
Note
The verbs that keep it company are tend to and approach, because nothing ever arrives. A sequence that tends to infinity has terms that eventually pass any bound you name. Topology also settles how many such points a space gets: the real line is usually extended by two, plus and minus infinity, while the complex plane receives one, reached by heading outward in any direction.
- 5A number so large compared with some characteristic number of a problem that, for practical purposes, it can be treated as infinite.
For the landscape shots, she set the lens to infinity so the distant ridgeline would be sharp.
Because the source is hundreds of focal lengths away, we can place it at infinity and treat the incoming rays as parallel.
Note
Nothing in this sense is actually endless: the quantity stays finite, and the word is a license to ignore its exact size. Optics shows why that is safe: an object far beyond a lens's focal length is said to be at infinity because moving it farther barely shifts where the image forms. With the idealized limit point the same phrase is exact; here it is a working approximation.
Practice
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Origin
From Middle English infinite, from Old French infinité, from Latin īnfīnitās ("unlimitedness"). The Latin word combines the negative prefix in- ("not"), fīnis ("end"), and the noun-of-state suffix -tās.