Difference between revisions of "Transfinite sequence"
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| + | $#A+1 = 8 n = 0 | ||
| + | $#C+1 = 8 : ~/encyclopedia/old_files/data/T093/T.0903710 Transfinite sequence | ||
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| − | A mapping of an interval | + | {{TEX|auto}} |
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| + | ''of elements of a given set $ X $'' | ||
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| + | A mapping of an interval $ [ 0, \beta ) $ | ||
| + | of (transfinite) ordinal numbers into $ X $( | ||
| + | cf. also [[Ordinal number|Ordinal number]]). By an element, or term, of the transfinite sequence $ f: [ 0, \beta ) \rightarrow X $ | ||
| + | is meant an ordered pair $ ( \alpha , x) $, | ||
| + | where $ \alpha \in [ 0, \beta ) $ | ||
| + | and $ x= f( \alpha ) $; | ||
| + | this term is often denoted by $ x _ \alpha $. | ||
Latest revision as of 08:26, 6 June 2020
of elements of a given set $ X $
A mapping of an interval $ [ 0, \beta ) $ of (transfinite) ordinal numbers into $ X $( cf. also Ordinal number). By an element, or term, of the transfinite sequence $ f: [ 0, \beta ) \rightarrow X $ is meant an ordered pair $ ( \alpha , x) $, where $ \alpha \in [ 0, \beta ) $ and $ x= f( \alpha ) $; this term is often denoted by $ x _ \alpha $.
How to Cite This Entry:
Transfinite sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transfinite_sequence&oldid=49010
Transfinite sequence. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Transfinite_sequence&oldid=49010
This article was adapted from an original article by L.D. Kudryavtsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article