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 Jan 8 comment Counting how many possible images in an 800x500(3color) image. Yes, as I wrote above: The most significant byte would be 1, and the 1,200,000 other bytes would be 0. However note that you only need 1,2000,000 bytes to represent $256^{800*500*3}$ different values (which would, obviously, not include the value $256^{800*500*3}$; the highest representable value in 1,200,000 bytes is $256^{800*500*3}-1$). Jan 8 comment Counting how many possible images in an 800x500(3color) image. Looking again at the three-digit example, interpreting the digits as number gives numbers from $0$ to $999$. That are $1000$ numbers, but the number $1000$ itself is not among them; indeed, it's the first one that's too large to fit in three digits. Another way to see it is: If it were only the numbers $1$ to $999$, you'd have $999$ numbers. But additionally you've got the $0$, and thus one more. But $999$ is already the largest 3-digit number, so you get a four-digit number. BTW, to write a positive integer $n$ in base $b$, you always need $\lfloor\log n/\log b\rfloor + 1$ digits. Jan 8 comment Counting how many possible images in an 800x500(3color) image. Well, that expression indeed gives exactly $1\,200\,000$. However, consider the number of sequences of 3 decimal digits. There are $10^3=1000$ such sequences, but the number $1000$ already has 4 digits (but $\ln 1000/\ln 10=3$). Jan 8 comment Counting how many possible images in an 800x500(3color) image. Actually, you need $1\,200\,001$ bytes to represent that number: The first byte is $1$, all others are $0$. Jan 8 asked Functions where the pre-image of convex sets is convex Jan 8 revised Definition of Dirac Delta function on the surface of a unit sphere deleted 7 characters in body; edited title Jan 8 comment Is there a symbol for plus and minus as opposed to plus or minus? @TitoPiezasIII: The closest I could come up with is Module[{R},R[s_]:=(2 b^3-9 a b c + s Sqrt[-4(b^2 - 3 a)])^(1/3); (2/3a)(R[+1]+R[-1])] Jan 8 awarded Good Answer Jan 8 comment Prove that row rank of a matrix equals column rank Why did you not add your answer to an existing question, instead of writing a duplicate question? Jan 8 answered Basis for set of matrices with trace not equal 0 Jan 8 awarded Nice Answer Jan 7 answered Is there a symbol for plus and minus as opposed to plus or minus? Jan 2 answered Is it possible to draw this picture without lifting the pen? Jan 2 comment Is it possible to draw this picture without lifting the pen? You omitted an important (but obvious) condition: The graph must be connected! Dec 21 answered Even + Odd Function Dec 21 answered Have anyone ever thought of continuous analog Turing machine? Dec 21 comment Have anyone ever thought of continuous analog Turing machine? As far as I know, those analog computers were not universal computers, but purpose-built for specific problems. The point of the Turing machine is that it is universal. Dec 20 answered When is a mobius transformation its own inverse? Dec 20 revised Find the value of following complex number edited title Dec 20 comment $A \cap B$ = $A \cup B \iff A = B$ @dreamin: $A\subset A\cup B$ is a property of $\cup$. $A\cup B=A\cap B$ by assumption. $A\cap B\subset B$ is a property of $\cup$. Note that this proves only one direction, but the other direction works essentially the same.