Not all infinities are created equal
Georg Cantor's diagonalization argument proved that the infinity of real numbers is uncountably larger than the countable infinity of natural numbers, revealing different sizes of infinity.
In 1891, mathematician Georg Cantor proved that some infinities are vastly larger than others. He showed that while natural numbers (1, 2, 3...) form a 'countable' infinity, real numbers (including all decimals) are 'uncountably' infinite. Cantor's groundbreaking diagonalization argument demonstrated that you can't list all real numbers, even in an infinite sequence. This shattered the old idea of infinity as a single concept.
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