what 'box'? um.. on the interval [0,1] f(x)=0 only at x=0, everywhere else the value of f for an x will be the 1/n value x is less than or equal to..
i thought that meant in, say, [1/2,1], f(x)=1 , except at x=1/2
did i miss something?
Homework Statement
f:[0,1]→R where f(x)= 0 if x=0 and f(x)=1/n when 1/(1+n) < x ≤ 1/n, n \in N.
is f Riemann integrable
Homework Equations
R integrable only when L(f) =U(f)
L(f) = largest element of the set of lower sums for n partitions
U(f) = least element of the set of upper...
yea.. i kinda did.
I think i should start another one: how does one delete a pointless thread in PF?
hmm..
its just that the idea of throwing yourself to Earth at 37km with nothing but a pressure suit (and a parachute that only opens when you break the sound barrier) seems fantastic
yeah it does, which is why I asked. Whats wrong with it though? if someone could point out the flawed reasoning maybe it'd better my understanding of group theory.
Thanks for the link, the (ba)^{∞} proof was hilarious
Homework Statement
(ab)^{n}= a^{n}b^{n} for any 3 consecutive numbers n \inN
Homework Equations
for an abelian group G, ab=ba \foralla,b\inG
if a\inG, a has an inverse element also \inG such that aa^{-1} = e
The Attempt at a Solution
doesnt look right but here's the attempt...
hes attempting to break a record for the highest free fall (37km from the Earth's surface)
heres a link to a site about Joe Kittinger (who holds the current record at 31.3km)
http://testblog-testblog123456-testblog.blogspot.in/2011/11/dispatches-blog-supersonic-man-col-joe.html
so there's no difference between an infinite intersection and a finite intersection? :confused:
i guess that's because of the way the infinite sets are defined i.e. with respect to an n.
does anyone have an example of an ∞ intersection of open sets that's open?
Also does an ∞ intersection...
Homework Statement
to prove that a function bounded on [a,b] with finite discontinuities is Riemann integrable on [a,b]
Homework Equations
if f is R-integrable on [a,b], then \forall \epsilon > 0 \exists a partition P of [a,b] such that U(P,f)-L(P,f)<\epsilon
The Attempt at a...
does this have something to do with the for every ε part?
ie the diff between f_{n}(x) = 1/2 and f(1/n) = 0 is greater than some ε (ie ε < 1/2)
i think I've got it
Thank you Dick