Invisible wrote:
> Oh, I see. I thought it was going to say something more insightful than 
> that. (How the hell do you compute a limit or an integral anyway?)

Ahh, no nothing more insightful, just that it did address the major 
points you were worrying about.

Also, I'll assume you mean "how do you numerically compute a limit or 
integral?":

If it's a limit, just compute it for numbers as close as possible to the 
limiting value (or really really big numbers if the limiting value is 
infinite).  The closer (or the bigger) the number you compute it for the 
closer your answer will be.

If it's an integral do something like this: 
http://en.wikipedia.org/wiki/Riemann_sum

> But you can't compute an infinite product.

If the product converges (which it does, otherwise you couldn't define a 
number/function with it) then you can by definition get an arbitrarily 
good approximation by computing the product of the first n terms for a 
large enough n.

You might want to read up on these, they're pretty much fundamental to 
all of calculus and many many other ways of defining things over the 
real (or complex) numbers (Taylor expansions, Fourier series, numeric 
optimization and root finding, etc.):

http://en.wikipedia.org/wiki/Limit_(mathematics)
http://en.wikipedia.org/wiki/Limit_of_a_sequence

Out of curiosity have you ever had a calculus class?  I'd think that 
these things should have been covered there, and it makes me wonder if 
maybe the UK curriculum is somewhat different that what I'm used to.

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