10-O / Mathematical Lives
Original Edition
Cantor Diagonal Office
Some infinities do not fit on the list.
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Behind the designRead the optional note
Cantor’s diagonal argument shows that any proposed complete list of infinite binary sequences or real numbers must omit at least one entry constructed by changing the diagonal digits. The reals are therefore uncountable.
The office keeps an impeccable infinite register. The highlighted diagonal quietly manufactures the record that proves the register can never be complete.