Between 0.1 and 0.99999.... you use all numbers of N — AgentTangarine
1,2,3,....9999999.... — AgentTangarine
This is getting painful to watch. — jgill
Take the square {(x,y):0<x<1,0<y<1} and map it one-to-one to the line {r:0<r<1) by using the procedure implied by the simple example (.329576914..., .925318623...) <-> .39229537168961243...
You can figure it out if you stay off the Xmas grog long enough. Although you are a smart physicist and may be pulling our legs. You and Agent Smith can work this out. It cropped up in the course I used to teach in Intro to Real Analysis.
Hence, there are exactly the same "number" of points in the (section of) the plane and on the unit interval. Same cardinality.
5h — jgill
0-0.1] seems to contain less numbers than [0.1-0.99999...]: — AgentTangarine
Can you break up a continuous interval, like [0.1-1], up in real points? Like 0.1, 0.2, 0.3,...,0.91, 0.92,...,0.110, 0.111,...,0.1222, 0.1223,..., 0.2111, 0.2112,..., 0.24444, 0.24445, ...0,2023432, 0.2023433, ..., 0.655555, 0.655556,.......,0.999999999999.... — AgentTangarine
confidently throwing around specialist terminology. — SophistiCat
I think that would be fine. There's been plenty of discussions before about the nature of the continuum. Just try and keep it away from the mathematical equivalent of pseudoscience — fdrake
This is the same crank whose banning you were lamenting earlier because (he says) he is a physicist and we should be grateful for him being here to educate us... Be wary of unhinged bullshitters confidently throwing around specialist terminology. — SophistiCat
The fact that the line, plane or volume have the same cardinality is because of the attempt to reduce them to points — AgentTangarine
The bijection between R and RxR is not continuous — AgentTangarine
I was only there for seconds. It felt like an eternity. — Brazil nightclub fire survivor (2013)
This is getting painful to watch. A simple example shows that the "number" of points in the interior of a cube {p=(x,y,z):0<x<1,0<y<1,0<z<1} , is exactly the "number" of points on the line {r:0<r<1}:
1:1 correspondence demonstrated by r=.3917249105... <-> p=(.3795..., .921..., .140...)
Extending these ideas shows the cardinality of R^3 is the same as that of R. — jgill
Why is there not therefore a paradox? — hypericin
I was only there for seconds. It felt like an eternity. — Brazil nightclub fire survivor (2013)
I'm not sure what you exactly mean by "going right to number lines", but if you imply that "infinity" and "infiniteness" are normally connected to numbers (Math), I think that this is too much restricting. There are a lot of things we call "infinite", even if actually they are not, but only very huge in size, from simple to complex: a line, a circle, love, time, space, the Universe (although its infiniteness is still debatable), ... That is, anything the limits of which cannot be determined.Is there a way to describe various infinites without going right to number lines? Anything in real life to reference in terms of the infinite? — TiredThinker
Is there a way to describe various infinites without going right to number lines? Anything in real life to reference in terms of the infinite? — TiredThinker
Unbounded spaces e.g. Earth's surface, etc.Anything in real life to reference in terms of the infinite? — TiredThinker
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