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 Jul28 comment Trouble with filling out a Cayley table $u*u = p$. What is $u*u*u$? Jun8 awarded Constituent Jun8 awarded Caucus Jun8 answered Prove that the product of four consecutive positive integers plus one is a perfect square May9 revised Where does binary arithmetic/manipulation enter the mathematics/engineering curriculum? extra question May9 asked Where does binary arithmetic/manipulation enter the mathematics/engineering curriculum? Apr25 comment History of dot product and cosine The dot product as an explicit algebraic operation is not so necessary to the 'dischord of appearances', it is the $a d + b e + c f$ a decidedly open calculation in comparison to the obscurantist length of a vector and angle formula (requiring much more machinery). Any idea if this (what Hamilton knew) was popular before Gibbs? Apr10 comment How do you explain the concept of logarithm to a five year old? @DanNeely: Yes, you're right. There are many contexts where an explanation could work/be meaningful and useful to a 5 yar old (JohnS keeps coming up with good ones). I think I was caught up in the symbol manipulation. But I still think the simple 'number of digits' concept, which would totally work for older kids (8-10 yoa) would be obscurantist to even a curious 5 year old. Apr8 comment How do you explain the concept of logarithm to a five year old? To a -5- year old? Aren't you stretching the limits of relevance? Most (even bright) kids are only about to 'get' negative numbers (which is arguably a much prior concept (inverse of addition) that is much more accessible. If this is just for fun (for a child that can 'get' things), then @JohnS's example looks to be aan excellent idea with lo-tech/lo-conceptual overhead. Mar29 comment Bounding ${n \choose k}$ ${n \choose k}$ increases up to $k = \lfloor n/2 \rfloor$, then goes down. So you only really need to worry about the left side up to the max. Mar25 comment Pseudo Proofs that are intuitively reasonable Isn't everything rigorous until you throw some doubt on it (which further elucidation (notational conventions, development of concepts) makes more rigorous)? Feb28 revised Connecting finite automata and regular languages in teaching/applications added links Feb28 comment How to pronounce $\setminus$ But is that the way you in practice pronounce it? Feb28 comment “Binomial theorem”-like identities @anon: falling factorials are counting (iteratively) selection without replacement (and rising factorials do the same starting from the top). Feb25 asked Connecting finite automata and regular languages in teaching/applications Feb13 comment Category of Trees as sub-category of Category of Graphs @DamianSobota: you could make that a full answer rather than a comment. Dec4 comment A list of all algebras? Here's a WP list of algebras. Oct31 comment New to probability - Is this true? 20-sided die (and also 12-sided die) are notoriously non-random. Because the angles at the vertices and edges are so obtuse, even without deliberate modification, they are very easy to wear to the point where some sides are favored rather than others. A better physical device to get 1 through 12 would be to roll a 6-sided side and flip a coin: add 6 for tails and 0 for heads. But of course theoretically, leaving out 13 through 20 works just fine. Oct22 answered If both $P$ and $Q$ are true , how can I tell that $P$ implies $Q$? Oct17 comment How Many Theorems (Tautologies) Exist of 5, 6, 7, 8, and 9 Letters? @Mariano: Re: not counting NNx or C(x)(tautology) - you might be able to syntactically ignore the latter (if you enumerate a system that includes enumerating tautologies, but eliminating double negation seems hard (just intractable to create the system of equations). Anyway, might as well include those because those are viable tautologies.