Question

what is rigorous analysis (in real analysis)?

Answer 1

bone grinding, knuckle dragging, brute math i think. kinda like the way i solve stuff :)

Answer 2

i cant find a good definition of it, maybe the wolf has one

Answer 3

proving that proofs are proof worthy maybe?

Answer 4

using established proofs as a means of analysis?

Answer 5

when things are done rigorously...they are done percisely with no abiguity...

for example you dont use words like 'when x is close to a' you specifically say way you mean by that using formal language.

Answer 6

I usually hear real analysis called rigorous analysis, I think it's because things can be checked and double checked and truly proven. As opposed to some complex analysis that cannot be truly shown... knots come to mind.

Answer 7

lol ... mind knots

Answer 8

using the \(\epsilon,\delta\) definition of a limit to prove a limit is rigorous.

Answer 9

@amistre64 http://en.wikipedia.org/wiki/Knot_(mathematics)

Answer 10

no hand waving allowed :)

Answer 11

the incas i think counted with knots ...

Answer 12

its possible, but i doubt they ever did some of these silly infinite knots, or fractionally dimensional knots and other things that you know--dont exist, lol

Answer 13

ive heard of kleine bottles; is there a kline knot ?

Answer 14

klein bottles are the 3-space version of a mobius strip... but I'm sure theres some silly knot that is similar.

Answer 15

Can someone explain this to me,
If c is an isolated point of D, where D is a subset of R (real number), and D->R is a function. Then the function is continuous at c

Answer 16

http://www.kleinbottle.com/
i've wanted their klein beer mug for a while now... never got around to buying it though.

Answer 17

@2bornot2b
It's basically saying that c is part of D and D is made only of Real numbers, there's a function of R with respect to D and thus by induction R includes c and is continuous.

Though, I'm not sure that this is a true statement.

Answer 18

Is the following function continuous at c

Answer 19

Did you understand the figure?

Answer 20

Or do you want me to draw it again?

Answer 21

it appears to be in a hole. so it's impossible to determine for sure without the functions. Though, I'm not that good at this sort of thing, perhaps you should post this as a separate question so others will know you're asking it.