It's not infinite, it's finite, because the speed of light is finite.
Actually, when you look at one of these mirrors, the number of images will increase continuously at the velocity "c", so you can accept that its limit is infinite, but in other hand it's finite because the speed of light "c" is finite, it's a physical "optical" paradox.
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If 2 mirrors are placed perpendicular to each other then infinite no of images will be formed because image formed by one mirror will act as the object for the other and vice verse.
2 pairs of parallel lines.
A parallelogram has 2 pairs of parallel lines
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there are 2 sets of parallel lines in a square