… But the extended system was hugely controversial, and for good reasons. For example, Cantor found that
. His system was not commutative under addition. In fact, . We might be tempted to subtract from each side, but this would yield the nonsensical result . The controversy was a factor in Cantor’s mental breakdown and ultimate suicide.
(Thanks to investigators @replicakill and @mathematicus for a corrective tweak to this.)