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Show that the function defined by g(x)=x...

Show that the function defined by `g(x)=x-[x]` is discontinuous at all integral points which [x] denotes the greatest integer function.

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The given function is `{g}({x})={x}=[{x}]`

It is evident that `g` is defined at all integral points.

Let `n` be an integer.

Then,

`g(n)=n-[n]=n-n=0`

The left hand limit of `f` at `x=n` is,

...
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