Cantor's diagonal argument is a mathematical proof demonstrating that the set of real numbers is uncountably infinite, meaning its size is strictly larger than that of the set of natural numbers. This argument highlights the existence of different sizes of infinity by constructing a real number not listed in any given sequence of real numbers, thus proving that no bijection exists between natural numbers and real numbers.

Cantor's Diagonal Argument

Cantor's diagonal argument

A mathematical proof is a logical argument that establishes the truth of a mathematical statement beyond any doubt by using a sequence of deductive reasoning steps based on axioms, definitions, and previously established theorems. The rigor and structure of a proof ensure that the conclusion follows necessarily from the premises, making it a cornerstone of mathematical validity and understanding.

mathematical proof

set of real numbers

uncountably infinite

Size of real numbers

Size of natural numbers

different sizes of infinity

real number not listed

sequence of real numbers

Bijection between natural numbers and real numbers

Infinity

Infinite Set in the Context of Integers

Relevant Degrees

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