noun

• (uncountable) endlessness, unlimitedness, absence of a beginning, end or limits to size.
• (countable, mathematics) A number that has an infinite numerical value that cannot be counted.
  "Some of the most beautiful and thus appealing physical theories, including quantum electrodynamics and quantum gravity, have been dogged for decades by infinities that erupt when theorists try to prod their calculations into new domains. Getting rid of these nagging infinities has probably occupied far more effort than was spent in originating the theories."
• (countable, topology, mathematical analysis) An idealised point which is said to be approached by sequences of values whose magnitudes increase without bound.
• (uncountable) A number which is very large compared to some characteristic number. For example, in optics, an object which is much further away than the focal length of a lens is said to be "at infinity", as the distance of the image from the lens varies very little as the distance increases further.