Originally posted by Detonate
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You sure about that, I think we'd still be discussing in the trenches when the bajonets start swinging.
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Crystal clearOriginally posted by Qqmike View Post
I was just reading an article on probability theory (because it curdles my noodle(*), and I like to keep banging my head against such things until my noodle uncurdles), and I may have had an insight as a result:
As a non-mathematician, I would be quite happy to say that "1/∞ = 0", but a mathematician would be more likely to say something like "the limit of 1/x as x approaches ∞ = 0". Because I consider both statements to be semantically equal, I'd go with the former statement for brevity's sake.
(*) It curdles my noodle when I read things such as "Some events with zero probability (p = 0) are impossible, but some aren't".
(Edit) Typing a lemniscate "∞" is really tricky! Hold down CTRL, SHIFT and U, then release the U while continuing to hold down CTRL and SHIFT, then type 221E, then release the CTRL and SHIFT.sigpic "Let us think the unthinkable, let us do the undoable, let us prepare to grapple with the ineffable itself, and see if we may not eff it after all." -- Douglas Adams Comment
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I won't even touch the probability discussion as THAT was also one of my specialties for some years and my thesis was in applied prob.
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You are right about the "1/∞ = 0"! That hurts my eyes and my brain in ways you'll never know! But, of course, I know what it means as a shorthand. But ... oh jeez, here it comes ... how is the limit being approached? We are assuming it is obvious that we are letting x --> infinity through only positive values of x (and the zero is approached positively, 0+) . Not x --> MINUS infinity (and the zero is approached negatively, 0-)? Not the absolute value of x --> infinity? Or, more precisely, |x| --> + infinity? Which is it? My feeling is that if we want to talk about, to say, zero, just do it:
0
and avoid mentioning the specific computation of this zero. Or, do mention it and make it precise!An intellectual says a simple thing in a hard way. An artist says a hard thing in a simple way. Charles BukowskiComment
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On another forum. where we discuss the weather a lot I find CTRL,SHIFT, U 00B0 useful.°Originally posted by HalationEffect View Post
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When I was younger, it amused me greatly to say "for any real value of x, x/∞ = 0, and x/0 = ∞, therefore ∞0 = x, therefore all real numbers have the same value (because they can all be obtained by multiplying zero by infinity)".
Even though I knew it was wrong, I loved trolling people with it! <evil laugh>
I would completely neglect to mention that I knew full well that there are different infinities and that they aren't all the same (e.g. the infinite set of all positive integers contains within it the infinite set of all positive even integers and also the infinite set of all positive odd integers). One infinity is bigger than another?? <Head explodes>Last edited by HalationEffect; Jul 30, 2013, 09:07 AM.sigpic "Let us think the unthinkable, let us do the undoable, let us prepare to grapple with the ineffable itself, and see if we may not eff it after all." -- Douglas Adams Comment
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There's an easier way for the degree symbol: (first configure which key will be your compose key, if you haven't already - I've set mine to the right ALT key). COMPOSE o o. Gives the same result °.Originally posted by Detonate View PostOn another forum. where we discuss the weather a lot I find CTRL,SHIFT, U 00B0 useful.°
(Edit) Useful list of compose key sequences: http://www.hermit.org/Linux/ComposeKeys.htmlLast edited by HalationEffect; Jul 30, 2013, 09:23 AM.sigpic "Let us think the unthinkable, let us do the undoable, let us prepare to grapple with the ineffable itself, and see if we may not eff it after all." -- Douglas Adams Comment
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"One infinity is bigger than another?? "
Am I being baited?
http://en.wikipedia.org/wiki/Cardinal_number
There are infinitely many infinities (cardinal numbers).An intellectual says a simple thing in a hard way. An artist says a hard thing in a simple way. Charles BukowskiComment
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Hehe, again we have a case of "layman's abhorrent way of expressing a complex idea in a simplified form".Originally posted by Qqmike View Post
What I mean is, if you compare the infinite set of positive integers with the infinite set of positive even integers, the first set contains every number that is within the second set, but it also contains other numbers too, therefore it is, in that sense "bigger".sigpic "Let us think the unthinkable, let us do the undoable, let us prepare to grapple with the ineffable itself, and see if we may not eff it after all." -- Douglas Adams Comment
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>> if you compare the infinite set of positive integers with the infinite set of positive even integers, the first set contains every number that is within the second set, but it also contains other numbers too, therefore it is, in that sense "bigger".
The second set is a subset of the first set, yes, yet the two sets are the same (infinite) "size"; that is, they have the same cardinal number, each is just countably infinite (in "size"). Proof is trivial: Define the bijective mapping from the first set to the second by
x |--> 2xAn intellectual says a simple thing in a hard way. An artist says a hard thing in a simple way. Charles BukowskiComment
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Yep, that's where the exploding heads happen - with the notion that a subset of a set can be of the same size as that set. It's really counter-intuitive.sigpic "Let us think the unthinkable, let us do the undoable, let us prepare to grapple with the ineffable itself, and see if we may not eff it after all." -- Douglas Adams Comment
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I'm using a heavily modified xkb keymap, with ∞ mapped to 4th level 8-key [it looks like 8] (so I can type it with RightAlt (set as the 3rd-level modifier) + shift + 8, but forgot about it...it's obviously not a symbol I use every dayOriginally posted by HalationEffect View Post
I seem to recall you can define your own compose key sequences, too...but never tried that (there is no default compose sequence for ∞, right?)Comment
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As far as I can tell, that's right. If there is a default compose sequence for a ∞, then I couldn't find it for all my googling.Originally posted by kubicle View Postsigpic "Let us think the unthinkable, let us do the undoable, let us prepare to grapple with the ineffable itself, and see if we may not eff it after all." -- Douglas Adams Comment
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Sure, if that's what you want to call an argument over whether "equal" and "is defined to be" mean the same thing or not. Basically, that's what you freakazoids got down to.Originally posted by HalationEffect View Post
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We can also do a mean riverdance.Originally posted by SteveRiley View PostBasically, that's what you freakazoids got down to.Comment
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