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- factorial - Why does 0! = 1? - Mathematics Stack Exchange
The theorem that $\binom {n} {k} = \frac {n!} {k! (n-k)!}$ already assumes $0!$ is defined to be $1$ Otherwise this would be restricted to $0 <k < n$ A reason that we do define $0!$ to be $1$ is so that we can cover those edge cases with the same formula, instead of having to treat them separately We treat binomial coefficients like $\binom {5} {6}$ separately already; the theorem assumes
- Good book for self study of a First Course in Real Analysis
Does anyone have a recommendation for a book to use for the self study of real analysis? Several years ago when I completed about half a semester of Real Analysis I, the instructor used "Introducti
- Is zero positive or negative? - Mathematics Stack Exchange
So what IS the Holy Bible The Great Standardization Document of All Definitions for Mathematics? Because people are often fighting over different definitions of mathematical entities, 0 being one of such examples (French always start a flamewar when someone says 0 is not positive, because for French, 0 is positive and negative at the same time :P ) Same goes with definitions of angles, or
- Pisano periods and Artin conjecture - Mathematics Stack Exchange
Your numerical observations are correct and align precisely with the heuristic framework derived from Artin’s primitive root conjecture for algebraic numbers, combined with Chebotarev density and Kummer theory Let $\alpha = (1+\sqrt {5}) 2$ The Pisano period $\pi (p)$ is essentially determined by the multiplicative order of $\alpha$ (or $-\alpha^2$) in the appropriate finite field 1
- abstract algebra - Prove that 1+1=2 - Mathematics Stack Exchange
Possible Duplicate: How do I convince someone that $1+1=2$ may not necessarily be true? I once read that some mathematicians provided a very length proof of $1+1=2$ Can you think of some way to
- Proof: Open Ball is open - Mathematics Stack Exchange
This looks like a circular argument You prove that an open ball is open by showing that every point is contained in an open ball within the open ball By my understanding the topology of a metric space is DEFINED by taking "open" balls as a basis - so they are open by definition
- When 0 is multiplied with infinity, what is the result?
What I would say is that you can multiply any non-zero number by infinity and get either infinity or negative infinity as long as it isn't used in any mathematical proof Because multiplying by infinity is the equivalent of dividing by 0 When you allow things like that in proofs you end up with nonsense like 1 = 0 Multiplying 0 by infinity is the equivalent of 0 0 which is undefined
- What is the core issue with liking something or liking to like . . .
As the title says, what is exactly the battle between something you like, something you hate and something you 'like to like' ? Let's just say, Martin is a very bright student, in 5th grade, he sol
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