Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20070303 14:46:29
1/InfinityI made the statement in another topic that: I invite discussion "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #2 20070303 15:01:14
Re: 1/Infinitymeans That’s how it’s defined in standard real analysis. In other words, given any real positive number epsilon, you can always find a big enough positive number delta such that if you plug in any value of x greater than delta into ƒ(x), ƒ(x) will be within epsilon of 0. This avoids any mention of infinity, see? Last edited by JaneFairfax (20070303 15:08:19) #3 20070303 15:09:02
Re: 1/InfinityYes, exactly. It carefully avoids mentioning Real Infinity. Or what happens on infinity. Last edited by George,Y (20070303 15:09:33) X'(yXβ)=0 #4 20070304 09:26:09
Re: 1/InfinityIt's OK, I chose the words "commonly accepted" carefully, and think a discussion would be enlightening ... A naive interpretation of this would be (1+1/∞)^{∞} => (1+0)^{∞} => 1 (assuming (!) 1/∞ = 0, and also that 1^{∞} = 1 which is interesting in its own right) But plugging in large values of n gives us e=2.7182... getting consistently more accurate. Anyway, I will be writing this up somehow. In the meantime feel free to tear this apart. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #5 20070304 09:33:36
Re: 1/Infinity
There is no such thing as "on infinity". Functions are defined on the real numbers. Infinity is not a real number, and thus, not in the domain of functions. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #6 20070304 09:57:48
Re: 1/Infinity
Last edited by JaneFairfax (20070304 10:27:54) #7 20070304 10:25:21
Re: 1/InfinitySo I propose we give a welldefined definition to operations on infinity. Please note that any definition we give to operations on infinity will not be a binary operator (though that would be nice) as there are things such as indeterminate forms. We will leave these out and ignore them since there isn't really much we can do with them anyhow. So with this, we may remark that 1/infinity = 0 and 1^infinity = 1, but we can't say anything on what infinity / infinity is. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #8 20070304 12:05:27
Re: 1/InfinityThis is the page I am currently working on: Limits (An Introduction) "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #10 20070304 16:03:29
Re: 1/InfinityNice halfpage there. Why did the vector cross the road? It wanted to be normal. #11 20070304 20:16:54
Re: 1/InfinityThanks, mathsy ... umm talkative in a bad way? "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #12 20070304 21:00:38
Re: 1/InfinityDon't worry, I was just joking.
Why did the vector cross the road? It wanted to be normal. #13 20070304 21:25:24
Re: 1/InfinityAh yes good point, inanimate animation. Poetic license? "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #14 20070305 19:19:30
Re: 1/Infinity
Sorry Sir! I don't know you recently begin to censor the phrase " on infinity". Last edited by George,Y (20070305 19:30:55) X'(yXβ)=0 #15 20070305 21:12:46
Re: 1/Infinity
It may have been my intention, but ... did I succeed? "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #16 20070305 21:20:16
Re: 1/InfinityYou didn't. Neither did I stated you did. I meant "It (the definition of limit) avoids (discussing) what happens on infinity)". Last edited by George,Y (20070305 21:24:37) X'(yXβ)=0 #17 20070305 21:44:57
Re: 1/InfinityI just noticed that ... you subtracted 0.9 times the series from the series and were left with just a few terms. Neat work. "The physicists defer only to mathematicians, and the mathematicians defer only to God ..."  Leon M. Lederman #18 20070306 02:05:51
Re: 1/InfinityYes, that is exactly what I mean. Thank you for understanding. X'(yXβ)=0 