https://en.citizendium.org/wiki?title=Finite_and_infinite&feed=atom&action=historyFinite and infinite - Revision history2021-12-03T11:31:19ZRevision history for this page on the wikiMediaWiki 1.24.1https://en.citizendium.org/wiki?title=Finite_and_infinite&diff=100530833&oldid=prevPeter Schmitt: New page: In mathematics, the meaning of the terms '''finite''' and '''infinite''' varies according to context. {{subpages}} Essentially, '''finite''' means (similar to common usage) having a size...2009-07-15T22:30:10Z<p>New page: In mathematics, the meaning of the terms '''finite''' and '''infinite''' varies according to context. {{subpages}} Essentially, '''finite''' means (similar to common usage) having a size...</p>
<p><b>New page</b></p><div>In mathematics, the meaning of the terms '''finite''' and '''infinite''' varies according to context.<br />
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{{subpages}}<br />
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Essentially, '''finite''' means (similar to common usage) having a size <br />
which is ''bounded'' by a natural (or, equivalently, by a real) number.<br />
<br><br />
while '''infinite''' means ''unbounded'' in size or, more precisely, exceeding all natural (or real) numbers in size.<br />
<br><br />
(Often ''bounded'' and ''unbounded'' is used in the same sense.)<br />
<br />
But "size" may mean length, area, or the result of any other measurement,<br />
and thus the precise meaning of "finite" varies accordingly,<br />
but is often not explicitly given.<br />
Examples are:<br />
<br><br />
finite [[interval]], finite value, finite [[integral]],<br />
finite degree, finite [[dimension]], finitely often, etc.<br />
<br />
A special case of size is [[cardinality]],<br />
i.e., size with respect to the number of elements:<br />
<br><br />
[[finite set|'''finite''' sets]] have finitely many elements, i.e., 0 or 1 or 2 or 3 ... elements,<br />
<br><br />
[[countable set|'''infinite''' sets]] have more (i.e., at least an unlimited sequence of) elements.<br />
<br />
Thus the interval of real numbers between 0 and 1 is<br />
a ''finite interval'' and a ''bounded set'' because its ''length'' is bounded,<br />
but it is an ''infinite set'' because it contains infinitely many numbers.</div>Peter Schmitt