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  • Proof of $0x=0$ - Mathematics Stack Exchange
    Since $0$ is the neutral element for the addition, we have that $$0x = (0 + 0)x$$ and because of distributivity we find that $$ (0 + 0)x = 0x + 0x $$ Hence we find that $$0x = 0x + 0x$$ so $0x$ also acts as the neutral element Because of unicity of this element, we have that $0x = 0$ $\textbf {Edit:}$ As Will Jagy commented, you could also use that $0x$ has an additive inverse, denoted by
  • Is $0$ a natural number? - Mathematics Stack Exchange
    Inclusion of $0$ in the natural numbers is a definition for them that first occurred in the 19th century The Peano Axioms for natural numbers take $0$ to be one though, so if you are working with these axioms (and a lot of natural number theory does) then you take $0$ to be a natural number
  • Definition of $L^0$ space - Mathematics Stack Exchange
    $L^0$ is just a notation to refer to the weakness of the topology of convergence in measure It is not locally bounded but is metrizable if the underlying measure space is non-atomic and $\sigma$ -finite
  • How do I explain 2 to the power of zero equals 1 to a child
    My daughter is stuck on the concept that $$2^0 = 1,$$ having the intuitive expectation that it be equal to zero I have tried explaining it, but I guess not well enough How would you explain the
  • Limit of $x \\log x$ as $x$ tends to $0^+$ - Mathematics Stack Exchange
    as $x\log x<0$ for small $x>0$, and then using the substitutions $x\mapsto \frac {1} {x}$, $x\mapsto x^2$ The squeeze theorem then implies that the limit indeed is 0
  • definition - Why is $x^0 = 1$ except when $x = 0$? - Mathematics Stack . . .
    If you take the more general case of lim x^y as x,y -> 0 then the result depends on exactly how x and y both -> 0 Defining 0^0 as lim x^x is an arbitrary choice There are unavoidable discontinuities in f (x,y) = x^y around (0,0)
  • algebra precalculus - Zero to the zero power – is $0^0=1 . . .
    @Arturo: I heartily disagree with your first sentence Here's why: There's the binomial theorem (which you find too weak), and there's power series and polynomials (see also Gadi's answer) For all this, $0^0=1$ is extremely convenient, and I wouldn't know how to do without it In my lectures, I always tell my students that whatever their teachers said in school about $0^0$ being undefined, we
  • I have learned that 1 0 is infinity, why isnt it minus infinity?
    @Swivel But 0 does equal -0 Even under IEEE-754 The only reason IEEE-754 makes a distinction between +0 and -0 at all is because of underflow, and for + - ∞, overflow The intention is if you have a number whose magnitude is so small it underflows the exponent, you have no choice but to call the magnitude zero, but you can still salvage the
  • What does it mean to have a determinant equal to zero?
    Your answer is already solved, but I would like to add a trick If the rank of an nxn matrix is smaller than n, the determinant will be zero





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