Real parameter a

[topsquark]

How do physicists say "[imath]\forall \epsilon>0 \exists\delta : |x-a|\leq \delta \rightarrow |f(x)-b|\leq\epsilon[/imath]" ?

We ask a Mathematician!

-Dan

 

[blamocur]

Excuse me for intruding late into a long thread.

I am a great believer that it would help students if we stress in algebra that learning mathematics requires learning two types of language. One type has just one exemplar, namely the formal notation of mathematics. That is an international written language, and in its pure form involves no sounds at all. The second type is the technical vocabulary used to discuss mathematics and to translate mathematical notation into a natural spoken language. Each natural language has its own technical vocabulary for mathematics. I have no idea how to write or say the Japanese version of "inverse operation."

"f(x) is continuous at a" in English normally has the following meaning:

[math]f(a) \in \mathbb R \ \land f(a) = \lim_{x \rightarrow a}f(x)[/math]
It would help if we explicitly recognized the two types of language involved in mathematics.

Is this a continuous function at 0 : [imath]f(x) = {x} {\sin \frac{1}{x}}[/imath] ?

 

[JeffM]

Is this a continuous function at 0 : [imath]f(x) = {x} {\sin \frac{1}{x}}[/imath] ?

No. f(0) is not defined.