Wikipedia:Reference desk/Archives/Mathematics/2014 November 13

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November 13

Do you think the following sequence is accurate? if not why not?

Philosophy -> Logic -> Formal Logic -> First-order logic + Common mathematical axioms -> Modern mathematics

Thanks. Ben-Natan (talk) 03:57, 13 November 2014 (UTC)

What are the arrows supposed to mean here? Dmcq (talk) 11:15, 13 November 2014 (UTC)

It sounds like you are interested in Foundations_of_mathematics. For the connection between logic/axioms and modern math, you might enjoy reading about Principia_Mathematica, which was Bertrand Russell's attempt to formalize a set of axioms and rules of inference that would allow all mathematical truths to be derived. Spoiler alert: it didn't work, and cannot work, in part because of Gödel's_incompleteness_theorems, which were proven shortly after PM came out. Other related reading might be ZFC, but this is all pretty heavy stuff unless you already have a lot of mathematical knowledge and experience. If you can explain what you mean by the arrows, or otherwise specify the question, you might get better answers. SemanticMantis (talk) 17:34, 13 November 2014 (UTC)

Bertrand Russell had himself spoiled an earlier attempt to axiomatize mathematics by Gottlob Frege by means of Russell's paradox. Robert McClenon (talk) 21:09, 13 November 2014 (UTC)

Hello guys; My Mathematical knowledge is humble in comparison to most of the people here - I guess it's generally what's needed for a Statistics introduction course in most of the worlds' academic institutions. The arrows' mean is to follow to the current stage (and common form) of Mathematics, which is offcourse what we can name 'Modern Mathematics', which allegedly born out of the combination of Western Philosophy & West Asian mathematical theories - my goal is to know how seemingly I'm accurate in the above sequence. Ben-Natan (talk) 01:14, 14 November 2014 (UTC)

Well, these things all developed at the same time, so there's not really a linear order. Nobody quit doing philosophy because formal logic was invented. As for "modern math", that is too broad to be a useful term, in my opinion. E.g. Modern abstract algebra traces back to Galois, while modern set theory didn't get started until much later.Monstrous_moonshine is again much younger still. However, all of these topics are part of "modern math". There were also plenty of important mathematicians that didn't care much at all about conceptual foundations or logic and philosophy. It is true that most contemporary mathematics is based upon a formal system of axioms, though much of the whole chain of construction is often glossed over. For example, a student may learn how to construct the real numbers out of sets via Dedekind cuts, but once the idea has been demonstrated, it's often ignored or at least taken for granted in future studies. SemanticMantis (talk) 17:23, 14 November 2014 (UTC)

Riemann product

Is there a notion analogous to Riemann sums using a product rather than a sum? I have some ideas. For example, one could use $\exp(\int _{a}^{b}\ln(f(x))dx)$. Or if f represents the exponential growth constant over an infinitesimal time period then the effective interest rate would be $\prod \exp {x\ f(x)}$. Essentially this would generalize continuously compounding interest where the rate is not constant. Here "interest rate" could instead represent inflation, essentially any situation where one talks about an exponential growth rate but that rate varies over time and one wants to find the net rate over a time period. The first idea I have is actually used in Compound interest#Force of interest.

The fundamental theorem of calculus (when applicable) and the properties of exponents gives $\exp {\int _{a}^{b}\ln(f(x))dx}={\frac {\exp {F(b)}}{\exp {F(a)}}}$ where $F(x)=\int \ln(f(x))dx$, which is just as intuitive as with ordinary integration.--Jasper Deng (talk) 20:25, 13 November 2014 (UTC)

Please, check parentheses in your formulas above. Ruslik_Zero 20:42, 13 November 2014 (UTC)

See product integral and multiplicative calculus. (But be warned that although this is a real, albeit minor, subject in mathematics, Wikipedia's treatment of it has been systematically skewed by one very persistent crackpot.) Sławomir Biały (talk) 20:50, 13 November 2014 (UTC)

Accounting Principles

Based on the information given, which method of accounting for bad debits is Darby Company using-the direct write-off method or the allowance method? How can you tell?

Never mind bad "debits", you should credit us with enough nous to see a request to do (incompletely specified) homework.→86.171.209.142 (talk) 23:17, 13 November 2014 (UTC)

Have you looked up explanations of direct write-off method [1] and allowance method [2]? SemanticMantis (talk) 17:16, 14 November 2014 (UTC)