BlueRaja - Danny Pflughoeft
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 Nov 24 awarded Good Answer Oct 11 comment Implication in mathematics - How can A imply B when A is False? When $B$ is true, $A \Rightarrow B$ is never false. If it's not false, it must be true. Oct 4 awarded Famous Question Sep 29 comment Counting numbers in a sequence - explain “Add 1 before you're done” rule Counting from $0$ to $1$, we get $\{0,1\}$ which contains two numbers, even though $1-0=1$ Sep 17 awarded Notable Question Sep 15 comment How to self learn mathematics if you can't buy the books? I have done this before, it works well. Sep 9 comment Proof that doctors could relate to Not a proof, but Simpson's Paradox is something all (medical) doctors should understand. Sep 6 comment I roll a die repeatedly until I get 6, and then count the number of 3s I got. What's my expected number of 3s? Anytime you roll something other than a 3 or a 6, you can pretend it never happened. Thus, you can treat it like a coin-flip, and then you're asking "If I flip a coin until I get heads, what's the expected number of tails?" which is one less than the expected number of flips to get a head. Sep 5 comment Does every irrational number contain arbitrarily long sequences of some digit? Take pi and between every pair of digits that are the same, insert a different digit. Aug 13 comment Do people whose native languages are read right-to-left experience mathematical statements differently? In programming and in algorithms papers, a = b and b = a mean opposite things (because = is used to assign, rather than define, a variable). Additionally, in CS courses you'll often see notation like $2x^2 = O(x^2)$, while the reverse statement is meaningless. The latter example is really an abuse of notation, though (a more precise notation would be $2x^2 \in O(x^2)$) Jul 21 awarded Yearling Jul 13 awarded Autobiographer Jul 12 comment How to prove that the Fibonacci sequence is periodic mod 5 without using induction? @Timbuc: The natural numbers can be defined inductively - are you claiming all proofs about natural numbers are inductive proofs? Jun 27 comment Easy math proofs or visual examples to make high school students enthusiastic about math Jun 3 comment Name of the highest power of 2 smaller than or equal to a given number @Morwenn: "Bit length" works perfectly fine with Gray codes, what makes you think it doesn't? The wikipedia article even uses the equivalent term "bit width" at the top of the page. Jun 2 comment Arc Length of Bézier Curves A derivation of another (obviously equivalent) closed-form can be found here May 20 comment Way to compare three numbers with an algorithm. To account for the relative differences, divide by the mean (or median). This is called relative standard deviation May 17 comment Are there mathematical objects that have been proved to exist but cannot be described in words? By this same reasoning, there are some numbers that are not computable. May 14 comment Expected return value of a recursive probabilistic function In retrospect, a function with infinite expected value seems not-so-surprising. Take for example while(random() > 0.5) returnVal *= 2. The expected return value is $1/2 + 2/4 + 4/8 + \ldots = 1/2 + 1/2 + 1/2 + \ldots$ May 14 accepted Is concatenation of digit-strings transitive?