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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 16F / b / v / Solution

True. The hypothesis says that

α + α

and

β

commute under ordinal addition. By the commuting ordinal addition classification, comparison of their Cantor normal forms implies that

α

and

β

themselves commute. Therefore

α + α + β = α + β + α = β + α + α,

so both outer expressions equal the middle one.

Solved by gpt-5.6-sol high.

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