Galaxies come in many sizes. The Milky Way is big, but some galaxies, like our Andromeda Galaxy neighbor, are much larger. The universe is all of the galaxies – billions of them! Our Sun is one star among the billions in the Milky Way Galaxy.

The universe encompasses all of space, time, matter, and energy. The universe contains everything that exists, from particles of matter smaller than an atom to the largest stars.

The Universe is thought to consist of three types of substance: normal matter, ‘dark matter’ and ‘dark energy’. Normal matter consists of the atoms that make up stars, planets, human beings and every other visible object in the Universe.

The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them.

Although the concept of infinity has a mathematical basis, we have yet to perform an experiment that yields an infinite result. The universe could be infinite, both in terms of space and time, but there is currently no way to test whether it goes on forever or is just very big.

Cantor defined two kinds of infinite numbers: ordinal numbers and cardinal numbers. Ordinal numbers characterize well-ordered sets, or counting carried on to any stopping point, including points after an infinite number have already been counted.

Cantor showed that there’s a one-to-one correspondence between the elements of each of these infinite sets. Because of this, Cantor concluded that all three sets are the same size. Mathematicians call sets of this size “countable,” because you can assign one counting number to each element in each set.

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By Kevin Hartnett. Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.

The symbol for infinity is ∞, a horizontal 8. It was invented by John Wallis (1616–1703) who could have derived it from the Roman numeral M for 1000.

Irrational numbers aren’t rare, though. In fact, there is what mathematicians call an uncountably infinite number of irrational numbers. Even between a single pair of rational numbers (between 1 and 2, for example) there exists an infinite number of irrational numbers.