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  • yetAnotherUser@feddit.de
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    1 year ago

    Not quite. It’s somewhat annoying to work with infinities, since they’re not numbers. Technically speaking, ∞ + ∞ is asking the question: What is the result of adding any two infinite (real) sequences, both of which approaching infinity? My “proof” has shown: the result is greater than any one of the sequences by themselves -> therefore adding both sequences produces a new sequence, which also diverges to infinity. For example:

    The series a_n = n diverges to infinity. a_1 = 1, a_2 = 2, a_1000 = 1000.

    Therefore, lim(n -> a_n) = ∞

    But a_n = 0.5n + 0.5n.

    And lim(n -> ∞) 0.5n = ∞

    So is lim(n -> ∞) a_n = 2 • lim(n -> ∞) 0.5n = 2 • ∞?

    It doesn’t make sense to treat this differently than ∞, does it?