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  • Is $0$ a natural number? - Mathematics Stack Exchange
    Pros of considering 0 not to be a natural number: generally speaking 0 is not natural at all It is special in so many respects; people naturally start counting from 1; the harmonic sequence 1 n is defined for any natural number n; the 1 st number is 1; in making limits, 0 plays a role which is symmetric to ∞, and the latter is not a
  • Justifying why 0 0 is indeterminate and 1 0 is undefined
    0 0 = x 0 0 = x 0x = 0 0 x = 0 x x can be any value, therefore 0 0 0 0 can be any value, and is indeterminate 1 0 = x 1 0 = x 0x = 1 0 x = 1 There is no such x x that satisfies the above, therefore 1 0 1 0 is undefined Is this a reasonable or naive thought process? It seems too simple to be true
  • Seeking elegant proof why 0 divided by 0 does not equal 1
    10 Several years ago I was bored and so for amusement I wrote out a proof that 0 0 0 0 does not equal 1 1 I began by assuming that 0 0 0 0 does equal 1 1 and then was eventually able to deduce that, based upon my assumption (which as we know was false) 0 = 1 0 = 1
  • Is $0^\\infty$ indeterminate? - Mathematics Stack Exchange
    Is a constant raised to the power of infinity indeterminate? I am just curious Say, for instance, is $0^\\infty$ indeterminate? Or is it only 1 raised to the infinity that is?
  • Show that ∇· (∇ x F) = 0 for any vector field [duplicate]
    The most brutally simple approach: Write out the curl of a generic F = (Fx,Fy,Fz) F → = (F x, F y, F z), and then take its divergence The only assumption required is that all partial derivatives commute, e g
  • Is zero odd or even? - Mathematics Stack Exchange
    Some books say that even numbers start from $2$ but if you consider the number line concept, I think zero($0$) should be even because it is in between $-1$ and $+1$ (i e in between two odd numbers)
  • What does it mean to have a determinant equal to zero?
    After looking in my book for a couple of hours, I'm still confused about what it means for a (n × n) (n × n) -matrix A A to have a determinant equal to zero, det(A) = 0 det (A) = 0 I hope someone can explain this to me in plain English
  • What is $\\gcd(0,a)$, where $a$ is a positive integer?
    I have tried gcd (0, 8) in a lot of online gcd (or hcf) calculators, but some say gcd (0, 8) = 0, some other gives gcd (0, 8) = 8 and some others give gcd (0, 8) = 1 So really which one of these is correct and why there are different conventions?


















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