[in a cabin in the mountains, Jim wakes up and bangs his head on the table he was sleeping under]
Alex Rieger: Jim, are you alright?
"Reverend" Jim Ignatowski: Yeah...uh ... who are you?
Alex Rieger: I'm Alex. We're friends, we work together.
"Reverend" Jim Ignatowski: What? are we, lumberjacks?
Alex Rieger: No, we're cabdrivers.
"Reverend" Jim Ignatowski: I bet we don't do much business up here!
In the real number system, a sequence or series isn't said to be equivalent to a real number unless it converges to that real number as a limit. Converging is rigorously defined, based on the ability to choose and arbitrarily small number (usually represented as "epsilon") and prove the sequence or series comes within epsilon of that limit. 1, 0, 1, 0, 1, ... doesn't converge. It never comes within 1/3rd of 1/2.
Taking the average to shoe-horn a non-convergent sequence into a real number has no foundation in number theory. But we can't challenge the assertion that that's a good thing to do, because it's a video, a one-way communication, not a dialog. Proofs have to stand up to challenges.
This is not number theory. It's numerology, finding patterns in numbers and thinking to have discovered something profound. Numerology drove John Forbes Nash to thinking the universe was talking to him and actually hearing voices. Of course, this guy isn't within 50 IQ points of Nash, but he's fascinated by patterns in numbers, so he's walking down the same seductive path.
9 comments:
All this stuff makes me a little negative.
Most nonsense is amazing ...
1-1+1-1+1-1+1... isn't 1/2.
In the real number system, a sequence or series isn't said to be equivalent to a real number unless it converges to that real number as a limit. Converging is rigorously defined, based on the ability to choose and arbitrarily small number (usually represented as "epsilon") and prove the sequence or series comes within epsilon of that limit. 1, 0, 1, 0, 1, ... doesn't converge. It never comes within 1/3rd of 1/2.
Taking the average to shoe-horn a non-convergent sequence into a real number has no foundation in number theory. But we can't challenge the assertion that that's a good thing to do, because it's a video, a one-way communication, not a dialog. Proofs have to stand up to challenges.
This is not number theory. It's numerology, finding patterns in numbers and thinking to have discovered something profound. Numerology drove John Forbes Nash to thinking the universe was talking to him and actually hearing voices. Of course, this guy isn't within 50 IQ points of Nash, but he's fascinated by patterns in numbers, so he's walking down the same seductive path.
Turn back, friend! Turn back!
Oops, "... an arbitrarily small", sorry.
"1-1+1-1+1-1+1... isn't 1/2."
Exactly.
All based on a faulty premise.
All I know about infinity is that it's too large, by half.
Or, something like that.
(I live in a double-infinity world.)
.
Yeah, infinity is at least 7 or 8 more than I'll abide.
In fact, I don't even enjoy approaching infinity anymore.
I count pudding with my toes
when I finish my theorem I will send you a copy. Lumberbrudi might like it.
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