Talk:Sequence: Difference between revisions
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imported>Catherine Woodgold (defined on the natural numbers) |
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== defined on the natural numbers == | == defined on the natural numbers == | ||
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:''"Formally, given any set ''X'', an infinite sequence is a function (''f'', say) defined on a subset of [[natural numbers]] with values in ''X''. "'' | :''"Formally, given any set ''X'', an infinite sequence is a function (''f'', say) defined on a subset of [[natural numbers]] with values in ''X''. "'' | ||
to this: | to this: | ||
:''"Formally, given any set ''X'', an infinite sequence is a function (''f'', say) defined on the [[natural numbers]] <math>{1,2,3,...}</math>, with values in ''X''. "'' | :''"Formally, given any set ''X'', an infinite sequence is a function (''f'', say) defined on the [[natural numbers]] <math>\{1,2,3,...\}</math>, with values in ''X''. "'' | ||
(I'm not sure whether to include zero in the natural numbers.) --[[User:Catherine Woodgold|Catherine Woodgold]] 08:12, 28 April 2007 (CDT) | (I'm not sure whether to include zero in the natural numbers.) --[[User:Catherine Woodgold|Catherine Woodgold]] 08:12, 28 April 2007 (CDT) | ||
::Done. --[[User:Catherine Woodgold|Catherine Woodgold]] 10:14, 29 April 2007 (CDT) | |||
== Simple example? == | |||
This is given as a "simple example" of a sequence of complex numbers: | |||
:<math>1 + i, 2 - 5i, 5 - 2i</math> | |||
How about a simpler example, where it's easy to predict the next term? e.g. | |||
:<math>1 + i, 2 + 3i, 3 + 5i</math> | |||
--[[User:Catherine Woodgold|Catherine Woodgold]] 08:20, 28 April 2007 (CDT) | |||
::I wouldn't object any proposed changes, the formal definition above included (well I thought a while about this definition and I think there would be no harm if the term "subset" gets deleted). As for 0 in naturals, nothing is "globally" decided, so probably both solutions are possible (I'd start with 1).--[[User:Aleksander Stos|AlekStos]] 11:55, 28 April 2007 (CDT) | |||
:::Done. Thank you. --[[User:Catherine Woodgold|Catherine Woodgold]] 10:15, 29 April 2007 (CDT) | |||
Latest revision as of 14:32, 14 November 2007
defined on the natural numbers
I would like to change this:
- "Formally, given any set X, an infinite sequence is a function (f, say) defined on a subset of natural numbers with values in X. "
to this:
- "Formally, given any set X, an infinite sequence is a function (f, say) defined on the natural numbers , with values in X. "
(I'm not sure whether to include zero in the natural numbers.) --Catherine Woodgold 08:12, 28 April 2007 (CDT)
- Done. --Catherine Woodgold 10:14, 29 April 2007 (CDT)
Simple example?
This is given as a "simple example" of a sequence of complex numbers:
How about a simpler example, where it's easy to predict the next term? e.g.
--Catherine Woodgold 08:20, 28 April 2007 (CDT)
- I wouldn't object any proposed changes, the formal definition above included (well I thought a while about this definition and I think there would be no harm if the term "subset" gets deleted). As for 0 in naturals, nothing is "globally" decided, so probably both solutions are possible (I'd start with 1).--AlekStos 11:55, 28 April 2007 (CDT)
- Done. Thank you. --Catherine Woodgold 10:15, 29 April 2007 (CDT)
- I wouldn't object any proposed changes, the formal definition above included (well I thought a while about this definition and I think there would be no harm if the term "subset" gets deleted). As for 0 in naturals, nothing is "globally" decided, so probably both solutions are possible (I'd start with 1).--AlekStos 11:55, 28 April 2007 (CDT)