Changes

:Deborah while the previous article was easier to read, it was easier to read because it was wrong. [[User:DanielB|DanielB]] 00:04, 4 July 2008 (EDT)

:Deborah while the previous article was easier to read, it was easier to read because it was wrong. [[User:DanielB|DanielB]] 00:04, 4 July 2008 (EDT)

== Funtion vs. Sequence ==

== Function vs. Sequence ==

''Function should be first. It is more fundamental, even if it might be considered harder.''

''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 <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)