Bah! I need a good mathematical definition for "limit"

[phatj]

Stupid summer assignments... I'm on my last prob and I can't think of an effective definition of a limit

edit: I did search google... didn't find anything great.. yet

 

[bandana163]

How about this?
Limit = a barrier that cannot be bypassed, no matter how and how hard one tries.
Or: end of one's skills, abilities.

 

[clamum]

What's wrong with the dictionary?

 

[phatj]

OOPs... i meant a mathematical definition

 

[phatj]

OOPs... i meant a mathematical definition

 

[EngenZerO]

get a calculus book and copy down the derived formula of a limit. that should be a good enough definition...

 

[forkd]

limit= 6 beers

* can be surpassed but may be followed by loss of time, memory, job and sexual drive

 

[phatj]

lol^^

 

limit

In mathematics, a limit is a value toward which an expression converges as one or more variables approach certain values. Limits are important in calculus and analysis.
Consider the limit of the expression 2x + 3 as x approaches 0. It is not difficult to see that this limit is 3, because we can assign the value 0 to the variable x and perform the calculation directly. This sort of substitution is not possible, however, when we consider the limit of the expression 1/x - 2 as x increases without limit. (The expression for this is 'x approaches infinity.') It is apparent that 1/x approaches 0 as 1/x approaches infinity, although we cannot directly substitute infinity for x and calculate 1/x = 0. The limit, as x approaches infinity, of 1/x - 2 is therefore equal to -2.

From here.

 

[gopunk]

http://mathworld.wolfram.com/Limit.html

 

[EngenZerO]

here from my calc book

Definition of a Limit

Let f be a function defined at each point of some open interval containing 'a', except possibly at 'a' iself. Then a number L is the limit of f(x) as x approaches 'a' ( or is the limit of f at 'a') if for every number eplison > 0 there is a number delta > 0 such that

if 0 < | x - a | < delta, then |f(x) - L| < epsilon