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Proposition: Square of a Non-Zero Element is Positive in Ordered Fields

In any ordered field $(F,+,\cdot),$ if $x\in F$ and $x\neq 0$, then $x^2 > 0.$ If $x=0$ then $x^2=0$.

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Proofs: 1

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Proofs: 1

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References

Bibliography

  1. Knauer Ulrich: "Diskrete Strukturen - kurz gefasst", Spektrum Akademischer Verlag, 2001