Question

Prove that the negative of an irrationalnumber is an irrational number.
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Answer 1

$\tt \: let \: negative \: of \: an \: irrational \: be \: rational \: number. \\ \tt \: let \: j \: be \: an \: irrational \: number. \\ \tt \: therefore \: by \: the \:  assumption \: -j \: is  \: a \: rational \: number. \\ \tt \: since \: negative \: of \: a \: rational \: number \: is \: rational \\ \tt \: -(-j)= j \: is \: a \: rational \: number \:but \: we \: assumed \: j \: as \: an \: irrational \: number \\ \tt \: our assumption \: is \: wrong. \\ \tt \: therefore \:  so \: negative \: of \: an \: irrational \: number \: is \: irrational.$

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