since the disprove this is on math i just wondered how many sides are on a circle?

none

if you construct infinite-gon you'll get a circle

Not really P4 ... it will look like a circle but will never really reach it. If you consider it true you will answer infinite sides. but mathematically infinite is managed as a limit that is never really reached. otherwise you can made stupid demonstration like "the circumference of a circle is his diameter"... or other stupid stuff you can probably find on internet... So I answer 0.

Had you asked "How many sides does a circle have?" it's easy, 2, an inside and an outside.
But how many sides on a circle, it must be 1. Since a circle is 2 dimensional, it must be the top side you're looking for, the other side is beneath it.
Maybe I don't understand the question

Depends of the definition of a side In french, hte mathematical definition is not the common one ... So mathematically, 0. 2 should be a good answers the way you define it... hehe

zerø, because a "side" (too general) must have a beginning and an end. In the circle neither of the aforementioned exist. A second question to ask is, "If you cut a line (in the geometrical sense of the word) in half, insert a 5 cm segment does it get longer?"