Given the following two certainties:
a and b are real numbers and may be positive or negative.
Would it be possible to prove the following:
I tried product rule for limits and several other tricks, but I can't do it.
Nonetheless, intuitively this limit seems to be zero. For every a or b in
an infinite set there will be one with opposite sign (otherwise the sums
of a and b are not zero, but they always are), in fact each of the a or b
itself already occurs an infinite number of times. This means that also
every product ab occurs an infinite number of times, with both signs,
or the set would not be infinite. Am I right? Infinity is tricky business...
Is there a basic proof?
Thank you for any help...