Inequality involving Integration

Okay, its concerened with michael spivak's book.

there is this one inequality or rather symbol i see, ever since the definition. what exactly does the denote here?? i think it stands for some small distance error, or error in distance towards the y-axis, it does not entirely define what the \epsilon stands for.

also this inequality;

,

i know what the inequality represents but, just dont get the proof provided by the book. The other proofs are alright, though still very challenging indeed.

can anyone explain this concern i have?

thank you

Re: Inequality involving Integration

Quote:

Originally Posted by **Heinsbergrelatz**

Okay, its concerened with michael spivak's book.

there is this one inequality or rather symbol i see, ever since the

definition. what exactly does the

denote here?? i think it stands for some small distance error, or error in distance towards the y-axis, it does not entirely define what the \epsilon stands for.

also this inequality;

,

i know what the inequality represents but, just dont get the proof provided by the book. The other proofs are alright, though still very challenging indeed.

can anyone explain this concern i have?

thank you

You need to do a better job of defining your terms.

1. will be defined somewhere in the text, and is usually an arbitary positive number. You can usually think of it as being "small".

2. I assume that and and are upper and lower Riemann sums on some interval corresponding to some partition . In that case the point is that as the partition is refined the upper and lower sums approach one another and the limit is the Riemann integral.

3. From your questions it appears that you are focusing a bit too much on the symbol manipulations and not strongly enough on what they mean -- this is quite common in one's first exposure to rigorous mathematical analysis.

The idea behind limits is that the difference in the value of some function at two points can be made small (less than ) if the difference between and can be made sufficiently small (less than ).

Re: Inequality involving Integration

Quote:

Originally Posted by **Heinsbergrelatz**

Okay, its concerened with michael spivak's book.

there is this one inequality or rather symbol i see, ever since the

definition. what exactly does the

denote here?? i think it stands for some small distance error, or error in distance towards the y-axis, it does not entirely define what the \epsilon stands for.

also this inequality;

,

i know what the inequality represents but, just dont get the proof provided by the book. The other proofs are alright, though still very challenging indeed.

can anyone explain this concern i have?

thank you

The problem i have is none of those sympols mean anything to me.

I hate 'maths' like that'