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Apr
7
awarded  Excavator
Apr
7
revised Combinatorics: How to find the number of sets of numbers in increasing order?
Added expansion for binomial coefficient at end
Apr
7
suggested approved edit on Combinatorics: How to find the number of sets of numbers in increasing order?
Mar
31
comment The Curvy Rebound: One of the most interesting (Geometric) Probability problems.
@Kugelblitz: I would, except I really don't know them.
Mar
30
comment The Curvy Rebound: One of the most interesting (Geometric) Probability problems.
Just like to say that as the author of this question (!), Kugelblitz's intuitive assumptions regarding the possible ambiguities have all been spot on. For example, the red line does indeed rotate too - being 'fixed' to the circle. Regarding the infinitesimal small ball travelling along the red line forever; well, mathematically, that would only cover 0% of all possible angles, so any possible answer won't need to take that into account.
Mar
30
comment Probability of the Center of a Square Being Contained in A Triangle With Vertices on its Boundary
Wow my own question (Skytopia is my site) from years back ends up here. Yes, I'm the guilty culprit. Interesting to see all the responses!
Mar
7
comment The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
Be interesting to see his thoughts on 2-3 = 1, and 2/3 = 1.5 then to see if those too have any advantages over the usual interpretation.
Mar
7
awarded  Scholar
Mar
7
accepted The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
Mar
7
comment The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
Interesting suggestion to reverse the order. I was even thinking about using that suggestion for my calculator 'OpalCalc'. But I quickly tried + with - (and * with /), and it would seem having the base afterwards (like what I had) is consistent with that. Try it out, and see what you think: b + (b-x) != b - (b+x). Maybe there's some merit however to reversing the order for those too! So 5-4 would = -1 (not 1) in that system.
Mar
6
comment The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
@MarkBennet: I might just do that (and clarify what I mean whenever I do). It's not an unfair point, though I guess all new notation takes some getting used to.
Mar
6
revised The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
added 78 characters in body
Mar
6
comment The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
Relevant: What's the inverse operation of exponents?. The page claims TWO inverses. At least though you can get one of the inverses with the existing ^ operator with the addition of the divide operator: 1024^(1/5). However, log is needed to obtain 5 from the other two numbers (1024 and 4).
Mar
6
revised The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
added 2 characters in body
Mar
6
comment The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
@HenningMakholm: I was looking for good reasons why the idea was flawed, as well as insight into sensible math notation generally, beyond its evolution as a series of somewhat arbitrary historical choices. If as a side effect, it turns out to be a good idea, and so takes a small step to change the way we use notation, that wouldn't necessarily be a bad thing anyway.
Mar
6
comment The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
We can be flexible with regards to what the symbol should look like - the underscore symbol was just the first thing that I thought of. For computer use, I'd rather use the symbols than superscripts or subscripts anyway.
Mar
6
revised The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
added 302 characters in body
Mar
6
comment The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
@nayrb: Appreciated. I think historically, notation has evolved the way it has. But intelligent aliens (should they exist) may very well have a unique binary log symbol.
Mar
6
comment The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
Perhaps "inverse" was the wrong word. Regardless, it still completed the basic operator 'set' in my opinion.
Mar
6
comment The caret ^ symbol means exponentiation informally in math. Why not a symbol for log too?
You can still keep ln, log, or lg as separate common functions. You've already listed three common numbers used; having it as a binary operator is simply a generalization of that. At least in programming, I find I often have a need for an arbitrary base for the log operator.