| 释义 |
transfinite, a. (n.) Math.|trɑːnsˈfaɪnaɪt, træns-|
[f. trans- 4 + finite.]
Beyond or surpassing any finite number or magnitude: see quots. Also, as n., a transfinite number, etc.
1903Nature 3 Sept. 411/2 To readers unacquainted with [Cantor's] ‘Mengenlehre’, the introduction of transfinite numbers must appear rather startling. 1907Hobson Funct. Real Variable 177 Corresponding to a single transfinite cardinal number there is an infinity of transfinite ordinal numbers. 1907Athenæum 14 Sept. 307/2 The simplest conception of a transfinite number may be gathered from the following illustration. A man walks along a road at a uniform pace, and the distance he goes is divided into intervals—½ mile, 1/4 mile, 1/8 mile, and so on. The number of these intervals in the first mile is infinite, but the time taken is finite. We agree to regard the mile as ending with the ωth interval. If the next mile is divided in just the same way, then the intervals regarded as belonging to the same series will be the (ω + 1)th, (ω + 2)th, and so on. These numbers ω, ω + 1, ω + 2, are called by Cantor (who was the first to use them) transfinite ordinal numbers. |