Difference between revisions of "Talk:Limit (mathematics)"
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I'd like to object. The idea of the limit of a sequence is the more basic one - and it's taught first, I suppose. Generally, you introduce the limit of a function in a point via the limit of sequences: What does it mean (in your example) that <math>x \rightarrow 3</math>? It means, you look at all sequences <math>(x_1, x_2,...)</math> with <math>\lim x_n = x</math>. And if for all these sequences, the corresponding sequence <math>(f(x_1),f(x_2), ...)</math> converges to the same value <math>z</math>, you'd say that the function has limit in x. | I'd like to object. The idea of the limit of a sequence is the more basic one - and it's taught first, I suppose. Generally, you introduce the limit of a function in a point via the limit of sequences: What does it mean (in your example) that <math>x \rightarrow 3</math>? It means, you look at all sequences <math>(x_1, x_2,...)</math> with <math>\lim x_n = x</math>. And if for all these sequences, the corresponding sequence <math>(f(x_1),f(x_2), ...)</math> converges to the same value <math>z</math>, you'd say that the function has limit in x. | ||
But without this underlying concept, the expression <math> x \rightarrow 3</math> is unmotivated and baseless. --[[User:DiEb|DiEb]] 18:11, 17 August 2008 (EDT) | But without this underlying concept, the expression <math> x \rightarrow 3</math> is unmotivated and baseless. --[[User:DiEb|DiEb]] 18:11, 17 August 2008 (EDT) | ||
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| + | :I have put the order back the way you want it, but I hope to convince you that putting sequences later is the right thing. That is, do ordinary functions first, functions going to infinity at finite X second, and functions going to finite Y for infinite X third. This establishes the notion of "for every epsilon there is an M such that x > M get f(x) within epsilon". The sequence version of a limit is just a simple variation of that notion. | ||
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| + | :By the way, greetings. You and I seem to be the only math/science people left. Well, I notice that Lemonpeel has just come back, but things don't seem to be going well for him, and I suspect he will be out soon. My attempts to get the natural log page and the radioactivity page restored have met with no success at all, and I can't keep asking, since I'm on extremely thin ice. [[User:SamHB|SamHB]] 23:24, 19 August 2008 (EDT) | ||
Revision as of 03:24, August 20, 2008
who writes this stuff??--Lemonpeel 21:41, 3 July 2008 (EDT)
The math articles were written by random editors of conservapedia, I actually liked the earlier version of the article as it was easier to understand that the current version -- 
22:05, 3 July 2008 (EDT)
- Deborah while the previous article was easier to read, it was easier to read because it was wrong. DanielB 00:04, 4 July 2008 (EDT)
Function vs. Sequence
Function should be first. It is more fundamental, even if it might be considered harder. I'd like to object. The idea of the limit of a sequence is the more basic one - and it's taught first, I suppose. Generally, you introduce the limit of a function in a point via the limit of sequences: What does it mean (in your example) that ? It means, you look at all sequences with . And if for all these sequences, the corresponding sequence Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (f(x_1),f(x_2), ...)} converges to the same value Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z} , you'd say that the function has limit in x. But without this underlying concept, the expression Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x \rightarrow 3} is unmotivated and baseless. --DiEb 18:11, 17 August 2008 (EDT)
- I have put the order back the way you want it, but I hope to convince you that putting sequences later is the right thing. That is, do ordinary functions first, functions going to infinity at finite X second, and functions going to finite Y for infinite X third. This establishes the notion of "for every epsilon there is an M such that x > M get f(x) within epsilon". The sequence version of a limit is just a simple variation of that notion.
- By the way, greetings. You and I seem to be the only math/science people left. Well, I notice that Lemonpeel has just come back, but things don't seem to be going well for him, and I suspect he will be out soon. My attempts to get the natural log page and the radioactivity page restored have met with no success at all, and I can't keep asking, since I'm on extremely thin ice. SamHB 23:24, 19 August 2008 (EDT)