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Someone recently asked me why a negative $\\times$ a negative is positive, and why a negative $\\times$ a positive is negative, etc. I went ahead and gave them a proof by contradiction like this: As...
Since $\times$ is the official symbol for multiplying integers, this notation is in principle ambiguous: $2\times3=6$ would seem to imply $\Bbb R^ {2\times 3}=\Bbb R^6$, but the latter is not a space of matrices.
What is the notation for the set of all $m\\times n$ matrices?
How many times can I compress a file before it becomes corrupt? If the program you use to compress the file does its job, the file will never corrupt (of course I am thinking to lossless compression).
So cut $S^1 \times S^1$ twice, first at $\ {a \} \times S^1$ to get $ [a,b] \times S^1$ and cut it again. Now glue it together backwards and you get your definition of the torus.
6 If I flip a coin 10 times in a row, obviously the probability of rolling heads ten times in a row is $\left (\frac {1} {2}\right)^ {10}$. However, I am not sure how to calculate the exact odds that I will have at some point rolled heads 10 times in a row during a series of n flips.
For example, to repeat a range 3 times: Vertical: =REPTA(A1:C5, 3) Horizontal: =REPTA(A1:C5, 3, 1) Efficiency is relative to the size of the array. Smaller arrays will perform faster than larger arrays. The 5x3 array in the example shown above can output to column XFD without any noticeable calculation lag, using =REPTA(A1:C5, 5460, 1).
