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There is no number 'infinity' so we are obliged to ask for a limit:

lim pi-x as x tends to infinity. pi-x = 1/pix. As x increases pix increases 'much faster' making the fraction 1/pix smaller and smaller but always positive.

Thus when x is large the fraction will tend toward zero.

Incidentally, whenever you want to demonstrate these behaviours of functions for yourself may I suggest either of the following:

  • GeoGebra which is free and can be installed on your own computer
  • Wolfram-Alpha which is a web site that is free to use
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11y ago

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