Mathematicians often use the concept of infinity. But real life applications abound. For example, each of our lives may be considered infinite as one never knows birth or death, just what comes in between.
Which shows that infinity is one of those things that makes the brain hurt. Zeno's infinity paradox has inspired countless (see?) philosophers. The idea of adding up infinitely many infinitesimally small amounts to make something is the basis of calculus. In the stock market short sellers have a theoretically infinite loss potential.
German mathematician Georg Cantor proved that there are different orders of infinity: some infinities are larger than others. There are more real numbers, for example, than counting numbers, even though there is an infinite number of each.
Einstein proposed that the universe is infinite in three dimensions, and finite in four, somewhat following the math of Gabriel's Horn, which is infinite in surface area and finite in volume, making it possible to fill but not to wash.
Is your head hurting yet?