"... It is always possible to think of a larger number: for the number of times a magnitude can be bisected is infinite. Hence the infinite is potential, never actual; the number of parts that can be taken always surpasses any assigned number." [Physics 207b8]
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先看這個:
http://upload.wikimedia.org/math/8/6/6/86673317c91628dc8ea81622f0f9bdcd.png
應該咁讀:
"For any integer n, there exists an integer m > n such that P(m)".
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This is often called potential infinity; however there are two ideas mixed up with this. One is that it is always possible to find a number of things that surpasses any given number, even if there are not actually such things. The other is that we may quantify over infinite sets without restriction.
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數學上的 Infinity:
Infinity is the state of being greater than any finite (real or natural) number, however large.
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The word infinity comes from the Latin infinitas or "unboundedness." It refers to several distinct concepts (usually linked to the idea of "without end" or "bigger than the biggest thing you can think of") which arise in philosophy, mathematics, and theology.
In popular usage, infinity is usually thought of as something like "the largest possible number" or "the furthest possible distance"; hence naïve questions such as "what is the next number after infinity?" or "if you travel to infinity, what happens if you then go a bit further?".
In mathematics, "infinity" is often used in contexts where it is treated as if it were a number (i.e., it counts or measures things : "an infinite number of terms") but it is clearly a very different type of "number" than the integers or reals. Infinity is relevant to, or the subject matter of, limits, aleph numbers, classes in set theory, Dedekind-infinite sets, large cardinals, Russell's paradox, hyperreal numbers, projective geometry, extended real numbers and the absolute Infinite.
In philosophy, infinity can be attributed to space and time, as for instance in Kant's first antinomy. In both theology and philosophy, infinity is explored in articles such as the Ultimate, the Absolute, God, and Zeno's paradoxes. In Greek philosophy, for example in Anaximander, 'the Boundless' is the origin of all that is. He took the beginning or first principle to be an endless, unlimited primordial mass (apeiron). In Judeo-Christian theology, for example in the work of theologians such as Duns Scotus, the infinite nature of God invokes a sense of being without constraint, rather than a sense of being unlimited in quantity. In Ethics infinity plays an important role designating that which cannot be defined or reduced to knowlege or power.
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The Indian Jaina mathematical text Surya Prajnapti (c. 400 BC) classifies all numbers into three sets: enumerable, innumerable, and infinite. Each of these was further subdivided into three orders:
Enumerable: lowest, intermediate and highest
Innumerable: nearly innumerable, truly innumerable and innumerably innumerable
Infinite: nearly infinite, truly infinite, infinitely infinite
The Jains were the first to discard the idea that all infinites were the same or equal. They recognized different types of infinities: infinite in one and two directions (one dimension), infinite in area (two dimensions), infinite everywhere (three dimensions), and infinite perpetually (infinite number of dimensions).
希望可以幫你搞清楚咩係 infinite 同 infinity
詳細資料可看:
http://en.wikipedia.org/wiki/Infinite 
