this post was submitted on 27 Jun 2024
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[โ€“] [email protected] 12 points 1 month ago* (last edited 1 month ago) (1 children)

That's not how it's defined. 0.99.. is the limit of a sequence and it is precisely 1. 0.99.. is the summation of infinite number of numbers and we don't know how to do that if it isn't defined. (0.9 + 0.09 + 0.009...) It is defined by the limit of the partial sums, 0.9, 0.99, 0.999... The limit of this sequence is 1. Sorry if this came out rude. It is more of a general comment.

[โ€“] [email protected] -2 points 1 month ago

I study mathematics at university and I remember it being in the definition, but since it follows from the sum's limit anyways it probably was just there for claritie's sake. So I guess we're both right...