BTW, 137 is a fundamental constant because it's the hospital room Pauli died in.....
and i see you're no particle physicist :p "****, i couldn't be bothered dealing with all these annoying constants, let's just make life easy and make them all 1"
Suppose X is a metric space. A real valued function f defined on a metric space X is said to be of first baire class, if f is a pointwise, limit of a sequence of continuous functions on X.
A famous well know theorem asserts that if f is in the first baire class, then the set of points of discontinuity is of the first category.
Using this definition, can we characterize for what Metric Spaces, will the points of continuity of a real valued function, be dense in itself.
Sounds like a homework assignment. Are you sure you're phrasing that right?
They're talking about the lebesgue differentiation theorem & baire category theorem if memory serves me correctly?
Well where f is continuous, it must also be dense. Are you looking to prove that?
Is there any way to calculate the total number of possible Sudoku grids?
2 brain teasers i found interesting
Okay, so a hunter gets out of his cabin on morning and gets into his jet powered surface cruiser. He travels 4000 miles south; turns eastward and travels 4000 miles and finally turns north and cruises for 4000 miles, at the end of which he is back outside his cabin. Now he sees a bear standing outside his kitchen window and eyeing the pie he had left to cool.
What is the color of the bear ?
Give complete solution, with reasoning !
A Hungarian community of married mathematicians has the following tradition: should any man determine that his wife cheated on him, he shall hang himself at noon. The townsfolk being rather introverted, there is little gossip except when there is an affair. In such case everyone in the town hears about the infidelity by nightfall excepting, of course, the cheating couple's spouses. So if a man were to hear gossip but were not told of any affiar, he would determine, being the logical mathematician that he is, that his own wife was involved, and would thus hang himself at noon the next day.
On one particularly steamy summer day, nine women break their vows with other men. What is the result?