the.com/cardinality
the headcount of infinity, proving some endless things are bigger than other endless things.
means In mathematics, cardinality is the measure of how many elements a set contains — a way of counting size that works even for infinite sets.
from From Latin 'cardinalis,' meaning 'principal' or 'serving as a hinge,' from 'cardo,' a hinge or pivot — the thing everything turns on. The same root gives us 'cardinal numbers' (one, two, three — the counting numbers, as opposed to ordinals like first, second). Mathematicians borrowed this 'how many' sense in the late 19th century, when Georg Cantor was busy proving that infinities come in different sizes; 'cardinality' became the formal name for a set's headcount.
- diagonal proof
- Cantor showed reals outnumber counting numbers
- levels of infinity
- there are infinitely many infinite sizes
- aleph-null
- smallest infinity, the size of integers
- continuum hypothesis
- unprovable from standard math axioms
- databases
- counts unique values in a column
continuum hypothesis — cantor's 1878 problem: whether cardinality between integers and real numbers exists
aleph numbers — cantor's hierarchy of infinite cardinalities starting with ℵ₀ for countable sets