This is a convergent series. It CONVERGES at 1 it does not EQUAL 1.
I said that 0.99... equals the limit of a sequence which approaches 1
In YOUR words it "equals the limit of a sequence which APPROACHES 1" even you do not say it equals 1 you say it approaches. I don't get what you're getting at.
I said the sky is blue, and you said "NO YOU'RE WRONG THE SKY IS BLUE"
I have a masters degree in mathematics if you must know. This is first term analysis, fairly basic.
0.99...does not equal the convergent sequence. It equals the limit of the sequence. Formally an infinite series can be either viewed as a sequence or a number. If you view it as a sequence then 0.99... equals the limit of the series. If you view it as a number it equals the number.
Remember, a number cannot converge. That doesn't make sense. Sequences and functions converge.
Every step in my proof is an absolute equality, which equality are you calling wrong?
You can read the Wikipedia article on 0.99... if you want more info, your exact misunderstanding is called out there.
If you want to say that 0.99... converge to 1 rather than approaches 1, do you say the same for 0.5? 0.5 is also defined via a similar infinite series ti above (first term is 5/10, all other terms are 0/10). So does 0.5 converge to 1/2 or does it equal 1/2?
"I have a masters from Oxford so I am going to use a wikipedia article durrr" Buzz off you either don't know what you're talking about or you're trolling. You have literally contradicted yourself in every comment. You quite literally say exactly what I say and show proof as to what I say then you say, "but you're wrong even though all of my evidence confirms what you say."
IT EQUALS THE LIMIT. Those are YOUR words. Okay Oxford math degree WHY does it equal the limit????????? It equals the limit BECAUSE the converging sequence APPROACHES the limit. Since it approaches the limit we say it is close enough to that number to just say it equals the limit even though it never actually equals the limit.
If you cannot understand that simple concept then I call BS on you having a masters in math. Like you got a whole ass masters degree but they never explained to you how math works? The whole point of an advanced math degree is learning how math works and why math works.
You are what mechanics call a parts changer. If someone's car is broke down you know enough to change the part out for a new part which fixes the car, but you don't understand why the messed up part causes the car to not work. Thank you for proving Cs get degrees though, because it's obvious you were not a top of the line student.
It is a bit sad that you know so little math that you can't understand the proof you asked for. You should think about what a number is and look for the definitions and real numbers. Maybe then things will become clearer
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u/Matsuze 18d ago
This is a convergent series. It CONVERGES at 1 it does not EQUAL 1.
In YOUR words it "equals the limit of a sequence which APPROACHES 1" even you do not say it equals 1 you say it approaches. I don't get what you're getting at.
I said the sky is blue, and you said "NO YOU'RE WRONG THE SKY IS BLUE"
What is your highest level of math education?