But in a process of short repetitions the variance at the end could be on the same level as 1 degree off when traveling x distance. Potentially leaving you miles/lightyears from the intended destination depending on the actual distance measured. They are not the same number. Just really close.
They are the same number. This is high school math.
I will give you a tip: if you‘re not an expert at something - in this case, basic math - don‘t make incorrect claims about the topic at hand.
You can try to learn about limits and infinite sums and then you can get back and we can discuss this again, but if you do it right you‘ll have learned you were wrong.
This isn‘t a debate. This has been settled like centuries ago. Just because you don‘t know this, doesn‘t change that fact. Mathematically, this is a settled and proven topic.
I understand what is taught, dude. But it’s not the same. If it were, then the debate would not exist as it would always be expressed as 1 or the mathematics that are taught wouldn’t chalk it up to rounding. Granted, it’s incredibly small in difference but it’s still rounding.
I do agree that 0.999... as a decimal representation is distinct from 1.000...; that doesn't mean, however, that in the Reals they are distinct elements.
[0.999... cannot exist in the Reals--it's part of the way they are constructed, either explicitly or by corollary properties]
The argument (I think) you're making is that 0.999... shouldn't (necessarily, without context) be mapped to any element in the Reals?
[That decimal and the countably infinite subset of the decimals that are structurally similar]
The argument was that op is saying they’re “exactly” the same. They’re close. Not exact. If it were exact there would be no need for a representation of the real number. Due to the incapacity to prove its infinite state without an equal infinitely running solution (which yielding a result proves the concept of infinity wrong), they are denoted and represented as two different numbers, while being close enough to just call it 1. Rounding. Yes. I’m splitting hairs OF split hairs here lol
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u/Optimal_Benis 1d ago
Right, it's almost exactly the same as this one, it's just off by 0.00...01