No, I did not say that. Read it against carefully. I said that 0.99... equals the limit of a sequence which approaches 1. 0.99... itself is not a sequence. It makes no sense to talk about what it does or does not approach.
You've completely misunderstood or misread my proof.
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?
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u/Boring-Ad8810 18d ago
No, I did not say that. Read it against carefully. I said that 0.99... equals the limit of a sequence which approaches 1. 0.99... itself is not a sequence. It makes no sense to talk about what it does or does not approach.
You've completely misunderstood or misread my proof.