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 Apr 7 awarded Yearling Mar 29 awarded Good Answer Jan 6 comment What we're never taught explicitly "ab is equal to axb" isn't math; it's a matter of syntax being used for math, which consists of conventions. It is not an expression of mathematical truth, like that 2 and 3 are the prime factors of 5. "Order of operations" is the same thing: it has to do with mapping the syntax of an expression to meaning. Kids have to learn order of operations purely because the notation is ambiguous, with implicit associativity and precedence rules dictating the parse. (It's math in the sense that parsing a string is a form of math, but in that context, the activity isn't given a proper treatment). Dec 11 answered Does “Doing a thing to both sides of an equation” have a name? Nov 21 awarded Nice Answer Oct 28 awarded Quorum Sep 28 awarded Nice Answer Jun 3 comment Bijection between computable reals and rationals? Pi is computable only in the sense that there exists an algorithm for producing successive rational approximations of pi that monotonically improve (converge on pi). The algorithm never actually computes pi. From another perspective, the algorithm does not halt if asked to compute pi. An algorithm that doesn't halt isn't successfully computing anything: a computation has to terminate and produce a result. Apr 7 awarded Yearling Sep 24 awarded Autobiographer Aug 15 comment What should an amateur do with a proof of an open problem? This is ridiculous. Taking papers from some guy isn't jumping under a crazy bus. You're not a high security research compound and he's not a spy or terrorist. You're just academics, and he's just an enthusiast. Of course he has poor social skills, (thrusting papers at people and all) but how are the average social skills of those who work in the building? I bet a few of them have thrust flowers at a woman and ran away, haha. It's like you're rock stars and he's a shy groupie. Aug 15 comment What should an amateur do with a proof of an open problem? @Doc If you have a document notarized there is no point in mailing it to yourself. The post mark adds nothing over the notary's markings. Aug 1 comment Discrete mathematics and the big O problem. I don't get this either. All we need to show is there are some $m$ and $K$ such that $K|g(n)| \geq |f(n)|$ for $m \geq n$. I.e. for sufficiently large $n$, $g$ grows at least as fast as $f$, possibly within a constant factor $K$. Jul 31 answered Interest Theory- Annuity Withdrawals/Deposits Jul 29 revised Why is it that if I count years from 2011 to 2014 as intervals I get 3 years, but if I count each year separately I get 4 years? added 172 characters in body Jul 28 answered Why is it that if I count years from 2011 to 2014 as intervals I get 3 years, but if I count each year separately I get 4 years? Jul 15 comment Why Limit of $0/x$ is $0$, if $x$ approaches $0$? It's because for any values of $x$ other than $x = 0$, $\frac{0}{x}$ is zero. Thus no matter how close x gets to zero, the value of the expression is zero, as long as x doesn't reach zero. From this observation it pops out that the limit is zero. Jul 15 comment Explaining Infinite Sets and The Fault in Our Stars The English phrase "as many" implies counting. But the infinity is not countable, so this phrase does not apply in the sense of not connecting with that concept. You cannot put a segment of the real number line in a 1:1 correspondence with golf balls. Jul 15 comment Explaining Infinite Sets and The Fault in Our Stars You are also wrong, because you used the word "amount" to describe what is between 0 and 1. If you approach it that way, you will lose to the English majors: rightfully so. Jul 10 revised Are these 2 graphs isomorphic? deleted 3 characters in body