miracle173
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 Nov 22 comment Tigers and lions attack if they are hungry or threatened. I think 1. is funny but is wrong. A tigon is neither a tiger nor a lion (that is why it is called tigon). the same is true for ligers. So sentence 1. means: "if something is a tiger and a lion (which is not possible), then ..." Nov 22 comment Prove that $\pi>3$ using geometry How do you want to show something about pi if you have not definition of it? Nov 22 comment Prove that $\pi>3$ using geometry How is pi defined? Nov 20 comment Standard terminology for the “quotient of a quotient” so $q_k =n \mod m^{k+1}$ Nov 20 comment Show that the derivative of a function is not continuous you get $g'(x_n)= \frac{4}{\frac{\pi}{3}+ 2n\pi}\sin (\frac{\pi}{3}+ 2n\pi)$. This converges to $0$ Nov 20 comment Show that the derivative of a function is not continuous the title of our post is strange. Nov 20 comment Show that the derivative of a function is not continuous Yes, I think you are right Nov 20 comment Show that the derivative of a function is not continuous And what is $g'$ if $x \ne 0$? Did you already calculate it? Nov 20 comment Show that the derivative of a function is not continuous What is $f$? The same as $g$? Nov 19 comment How to simplify this composition function $g(x)=\underset{n\text{ times}}{\underbrace{f \circ f \circ f \circ f\circ f \circ \cdots\circ f}}(x)$? @Sanchayan: did you check this numerically? Nov 19 comment How to simplify this composition function $g(x)=\underset{n\text{ times}}{\underbrace{f \circ f \circ f \circ f\circ f \circ \cdots\circ f}}(x)$? @Sanchayan: what is $\sin^2(x)$: Is it $\sin(\sin(x))$ or $\sin(x) \cdot \sin(x)$ Nov 19 comment Permutation & Combination of letters @mihir: A picture of a text is not a good idea. This is not wanted here. He can type the original text to this post. If he needs assistance in formatting the text he will get help here. If one selects the context menu (right mouse button) 'Show -Math -> TeX Commands' of a TeX graphic, one can see the TeX command that generates this formula. TeX commands must be preceded and terminated by a dollar character (or two dollar characters is it should be positioned in a separate line) Nov 19 comment Permutation & Combination of letters @mihir: a picture of the letters and the envelopes? Nov 15 comment Is the minimum of two metrics is again a metric? what properties of a metric does the minimum have? Wha properies are you not able to prove? Nov 14 comment Show that $e^x=1+x+\frac{x^2}{2!}+…+\frac{x^n}{n!}+R_{n+1}$ and how is $e^x$ defined? Nov 12 comment Proof that $n^{n} \leq {(n+1)}^{n}$ to prove $(1+1/n)^n \geq 1^n$ by induction is almost the same as to prove $n^{n} \leq {(n+1)}^{n}$. So this is not a proof at all. But it seems that some readers are excited by the formulas Nov 12 comment Proof that $n^{n} \leq {(n+1)}^{n}$ to prove a simple statement by use a rather complex one seems not a very useful idea to me. Nov 12 comment Proof that $n^{n} \leq {(n+1)}^{n}$ and why $(1+1/n)^n \geq 1^n$? Because exponentiation is an increasing function? Then $(n+1)^n \geq n^n$ follows immediately. Nov 1 comment How many passwords can be formed? the throughput my connection to the internet is too weak. I cannot watch videos. but I think it is a sequence of points of a 3x3 grid such that a line segment that connects two consecutive points of this segment does not contain a point from this grid. But maybe I am wrong. Is the length of the sequence limited to 9? It would be fine if you precisely describe the password algorithm.. Nov 1 comment How many passwords can be formed? I have seen this but I don't have this. Can you describe the allowed passwords/patterns? What are consecutive dots?