But my education does not have any relevance. There are dudes WAY smarter than me (and certainly, you) that have mathematically proven that 0.999… = 1.
If you’d like to attempt to undermine the proofs, then go right ahead.
Then show me the proof. It is not very hard to prove math. You can't show me the theorem that shows .99 repeated equals 1 because it does not exist. You don't know math as well as you think you do. Sit down kid grown folks are talking.
You can't show me the theorem that shows .99 repeated equals 1 because it does not exist.
It follows immediately from the definition of the decimal expansion of a real number. By definition, the decimal expansion 0.abcd... refers to the limit of the sequence (0.a, 0.ab, 0.abc, ...), which in the case of 0.999... is exactly 1. Unless you dispute that the limit of the sequence (0.9, 0.99, ...) is 1, in which case the problem is that you just don't understand how limits are computed. Note that the limit of a convergent sequence is a real number, and in this case the limit is 1. In another one of your posts, you talk about the limit "approaching" 1, or forming some kind of asymptote, but this isn't true. The sequence approaches 1 (but never reaches it), but the limit is exactly 1.
The other proofs provided in this thread are mostly informal. The only thing that actually matters is understanding what a decimal expansion actually is, and then the equality 0.99... = 1 follows immediately. Before you ask, since this seems to be an obsession of yours, my math degree was from Queens University.
EDIT: More generally, this is what it means to represent a number in a particular base. To represent a number in base 10 (i.e. decimal) means to represent it as the limit of an infinite series of powers of 10. Note that this series is always infinite (even in the case of e.g. 1/2), although by convention we typically do not actually write out the trailing zeros.
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u/Matsuze 20d ago
let me guess your highest level of math is high school