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I'm with you 100% on all of those ambiguous terms. Conventionally, arcsin is now used. Log(x) edit: was presumed to be base 10 in most domains. Historically a c

I'm with you 100% on all of those ambiguous terms. Conventionally, arcsin is now used. Log(x) edit: was presumed to be base 10 in most domains. Historically a carry over from when logarithmic tables were used very often by those who operated in base 10 (*edit: read down for a historical exposition). Mathematicians were concurrently publishing with log(x) with e as the base. Calculators ultimately (legend has it, at least) formalized it to log = base 10 because engineers designed it not mathematicians, though it might just be angry mathematicians who perpetuate that lore ;). Some subsets of mathematics might use e as the implicit base, but it'd be obvious from the context of the paper. Ln is e. Lg is 10. I can honestly say though every single one of those ambiguities I had an issue with in the past. This post reignited latent of ire of mine which I haven't experienced since 16. Denotational semantics are important!

heinrich5991 11y ago
Most (all?) logs I encountered (in mathematics) were base e, simply due to the fact that base 10 isn't special in mathematics, but for base e, you have log' x = 1/x. Also, it seems very common to denote the inverse of a function (even sine or cosine) with f^-1. See also Wikipedia on that subject (https://en.wikipedia.org/wiki/Logarithm https://en.wikipedia.org/wiki/Logarithm): >The logarithm to base 10 (that is b = 10) is called the common logarithm and has many applications in science and engineering. The natural logarithm has the number e (≈ 2.718) as its base; its use is widespread in mathematics and physics, because of its simpler derivative. The binary logarithm uses base 2 (that is b = 2) and is commonly used in computer science.
- iheartmemcache 11y ago
  At least in the northeast US, ln(x) was the preferred nomenclature as to eliminate ambiguity. Again, it depends on what course you were taking. Lg and Ln. Log was explicitly avoided. In higher mathematics, f^-1 does not mean the inverse of a function, unless that function is injective. Most people are aware of that at that point, but it's still a mental hurdle you have to unlearn and can lead to dangerous composition errors. (Edit: since I can't respond to you, poster below me, I mean the latter of course) Historically, in yore days of sextants, slide rules and log tables, engineers could "lift" multiplication into addition with said log tables which were of convention base 10. For anyone who wasn't a peer in the Royal Society or a professor, that's how complicated math calculations were performed. Banks balanced books and calculated interest payments via tables like this, and the precision of your log tables had a mantissa (the original floating point error, heh).
  - schoen 11y ago
    > f^-1 does not mean the inverse of a function, unless that function is injective Do you mean that it has a different meaning for a non-injective function, or that it's undefined for a non-injective function because the non-injective function does not have an inverse?

heinrich5991 11y ago

Most (all?) logs I encountered (in mathematics) were base e, simply due to the fact that base 10 isn't special in mathematics, but for base e, you have log' x = 1/x. Also, it seems very common to denote the inverse of a function (even sine or cosine) with f^-1. See also Wikipedia on that subject (https://en.wikipedia.org/wiki/Logarithm https://en.wikipedia.org/wiki/Logarithm): >The logarithm to base 10 (that is b = 10) is called the common logarithm and has many applications in science and engineering. The natural logarithm has the number e (≈ 2.718) as its base; its use is widespread in mathematics and physics, because of its simpler derivative. The binary logarithm uses base 2 (that is b = 2) and is commonly used in computer science.

iheartmemcache 11y ago
At least in the northeast US, ln(x) was the preferred nomenclature as to eliminate ambiguity. Again, it depends on what course you were taking. Lg and Ln. Log was explicitly avoided. In higher mathematics, f^-1 does not mean the inverse of a function, unless that function is injective. Most people are aware of that at that point, but it's still a mental hurdle you have to unlearn and can lead to dangerous composition errors. (Edit: since I can't respond to you, poster below me, I mean the latter of course) Historically, in yore days of sextants, slide rules and log tables, engineers could "lift" multiplication into addition with said log tables which were of convention base 10. For anyone who wasn't a peer in the Royal Society or a professor, that's how complicated math calculations were performed. Banks balanced books and calculated interest payments via tables like this, and the precision of your log tables had a mantissa (the original floating point error, heh).
- schoen 11y ago
  > f^-1 does not mean the inverse of a function, unless that function is injective Do you mean that it has a different meaning for a non-injective function, or that it's undefined for a non-injective function because the non-injective function does not have an inverse?