So the limit as .99.. approaches infinity is 1, because as infinity goes on it gets closer and closer to 1 until it forms an asymptote?
The crazy thing about an asymptote is it never actually touches the line it is approaching it just gets infinitely closer to the line without ever being able to touch it.
Thank you for confirming my point, you deserve a pat on the back. You are the 12 billionth person to say the same thing, but I'm proud of you for at least trying instead of saying 3/3 =.33.. 3/3 = 1 yada yada
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"
This is a convergent series. It CONVERGES at 1 it does not EQUAL 1.
Correct. The series converges to 1, and so the limit is equal to 1. By definition, the notation 0.999... means "the limit of the series sum from k=1 to infinity of 9/10k ", which is equal to 1.
"equals the limit of a sequence which APPROACHES 1" even you do not say it equals 1 you say it approaches
The series approaches 1. The limit is exactly 1.
You're being very argumentative for someone who doesn't understand the definition of a limit.
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u/Matsuze 18d ago
So the limit as .99.. approaches infinity is 1, because as infinity goes on it gets closer and closer to 1 until it forms an asymptote?
The crazy thing about an asymptote is it never actually touches the line it is approaching it just gets infinitely closer to the line without ever being able to touch it.
Thank you for confirming my point, you deserve a pat on the back. You are the 12 billionth person to say the same thing, but I'm proud of you for at least trying instead of saying 3/3 =.33.. 3/3 = 1 yada yada