Curiosities · Foundation · 11 min
Sizes of infinity
Some infinite collections can be listed, while diagonal reasoning shows others cannot.
WHAT HAPPENS IF…Why does the flipped sequence evade every row?
Loading the mathematical model…
Visit integer pairs by increasing a+b, then by increasing a. Each diagonal is finite and each pair lies on one, so all pairs receive a finite index. In contrast, for any proposed list of infinite binary sequences, flipping the ith bit of row i constructs a sequence different from every listed row. The finite table illustrates that rule.
A detail that matters
This argument concerns binary sequences themselves, avoiding ambiguities in numeric expansions.
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