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Let f: N->Z be a function defined as f(x...

Let `f: N->Z` be a function defined as `f(x)=x-1000.` Show that `f` is an into function.

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Let `f(x)=y=x-1000`
`implies x=y+1000=g(y)` (say)
Here g(y) is defined for each `y in Z,` but `g(y) notin N " for " y le -1000.`
Hence `f` is into.
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