Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 n. Any number obtained by dividing an odd integer by two
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Examples

The numbers indicate volume flux in Sverdrups (106 m3/s) rounded to halfinteger values and are based on observations, with the exception of the surface outflow, which is adjusted to balance [1].

You will sometimes hear physicists explain that elementary particles come in two types: bosons, which have a spin of 0, 1, 2, or some other integer, and fermions, which have a spin of 1/2, 3/2, 5/2, or some other halfinteger.

This year they pick the spinstatistics theorem, which explains why elementary particles with halfinteger […] 22.

The fact that these sets of features come handinhand is the content of the spinstatistics theorem: particles that pile on have integer spins, particles that take up space have halfinteger spins.

If the universe obeys a symmetry called “supersymmetry” which relates bosons (integer spin particles) to fermions (halfinteger spin particles) then there must exist a supersymmetric partner for every particle we know about.

The spinstatistics theorem states that fermions have halfinteger spin.

Particles that have integer spin are called bosons, while those with halfinteger spin are called fermions.
The 2001 Nobel Prize in Physics  Information for the Public

This principle was later found to be associated with the symmetry of wave functions for particles of halfinteger spins in general, distinguishing what is now called fermions from the bosonic particles whose spins are integer multiples of.

Math tells us that all the fermionsparticles with halfinteger spinmust come from what is known as the

Spin has a direction and variable magnitude, but has to be a halfinteger: 0, 1/2, 1, 3/2, and so on.
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