Can N be constructed?
in [Logic]
|
Prev: "NO BOX CONTAINS THE BOX NUMBERS THAT DON'T CONTAIN THEIR OWN BOX NUMBER" ~ XEN
Next: "NO BOX CONTAINS THE BOX NUMBERS THAT DON'T CONTAIN THEIR OWN BOX NUMBER" ~ XEN
From: David R Tribble on 11 Jun 2010 14:05 WM wrote: >> Mathematics is physics (V. A. Arnold). > David R Tribble wrote: >> What is the physical focal length of a diopter 0 lens? > WM wrote: > What a pity that Arnold died. Now we will never get the answer. > Nevertheless, your question is physics with no doubt. Yes, it is a question about physics. So what is the physical focal length of a diopter 0 lens?
From: David R Tribble on 11 Jun 2010 14:06 WM wrote: >> My proof does not show which line is left. But it shows that finished >> infinity is a non-mathematical notion. Of course it is always the last >> line that is left, and it is impossible to get rid of a last line, >> though the contents of the last line may change as often as desired. > David R Tribble wrote: >> Non sequitur. If the contents of the last line changes, then >> obviously that must be a different last line. There must therefore >> be more than one line you call the "last line". > WM wrote: > The last line only temporarily deserves that name. Then there is no last line at all.
From: Simplane Simple Plane Simulate Plain Simple on 11 Jun 2010 14:06 On Jun 11, 8:14 am, WM <mueck...(a)rz.fh-augsburg.de> wrote: > On 11 Jun., 16:47, David R Tribble <da...(a)tribble.com> wrote: > > > WM wrote: > > > Mathematics is physics (V. A. Arnold). > > > What is the physical focal length of a diopter 0 lens? > > What a pity that Arnold died. Now we will never get the answer. > Nevertheless, your question is physics with no doubt. > > Regards, WM Colenbrander, Fletcher Low Vision Rehabilitation JCAHPO, Anaheim November 2003 14 APPENDIX II NOMOGRAM for VISUAL ACUITY CALCULATIONS LETTER SIZE VIEWING DISTANCE VISUAL ACUITY ICD 40 M -30 80 m 145 250 ft 1/0.5 2.0 115 20/10 60 m 140 200 ft 30 M -25 J#24 0.02 D 50 m 135 160 ft 1/0.6 1.6 110 20/12 40 m 130 120 ft 25 M -20 J#23 30 m 125 100 ft 1/0.8 1.2 105 20/16 25 m 120 80 ft 20 M -15 J#22 0.05 D 20 m 115 60 ft 1/1 1.0 100 20/20 16 m 110 50 ft 16 M -10 J#21 12 m 105 40 ft 1/1.2 0.8 95 20/25 Range of Normal Vision 0.10 D 10 m 100 30 ft 12 M -5 100 p J#20 8 m 95 25 ft 1/1.6 0.6 90 20/30 6 m 90 20 ft 10 M 0 80 p --- 5 m 85 16 ft 1/2 0.5 85 20/40 0.25 D 4 m 80 12 ft 8 M 5 60 p J#19 3 m 75 10 ft 1/2.5 0.4 80 20/50 2.5 m 70 8 ft 6 M 10 50 p J#18 0.5 D 2 m 65 6 ft 1/3 0.3 75 20/60 Near-normal Vision 1.6 m 60 5 ft 5 M 15 40 p --- 1.2 m 55 50 1/4 0.25 70 20/80 1 D 1 m 50 40 4 M 20 32 p J#17 80 cm 45 30 1/5 0.2 65 20/100 (16) 60 cm 40 25 3 M 25 24 p J#15 2 D 50 cm 35 20 1/6 0.16 60 20/120 2.5 D 40 cm 30 16 2.5 M 30 20 p J#14 3 D 30 cm 25 12 1/8 0.12 55 20/160 Moderate Low Vision 4 D 25 cm 20 10 2 M 35 16 p J#13 5 D 20 cm 15 8 1/10 0.1 50 20/200 6 D 16 cm 10 6 1.6 M 40 12 p J#12 8 D 12 cm 5 5 1/12 0.08 45 20/250 (11) 10 D 10 cm 0 4 1.2 M 45 10 p J#10 12 D 8 cm -5 3 1/16 0.06 40 20/300 (8,9) 15 D 6 cm -10 2.5 1 M 50 8 p J# 7 20 D 5 cm -15 2 1/20 0.05 35 20/400 Severe Low Vision (6) 25 D 4 cm -20 1.6 0.8 M 55 6 p J# 5 30 D 3 cm -25 1.2 1/25 0.04 30 20/500 (4) 40 D 2.5 cm -30 1 0.6 M 60 5 p J# 3 50 D 2 cm -35 0.8 1/30 0.03 25 20/600 60 D 1.6 cm -40 0.6 0.5 M 65 4 p J# 2 80 D 1.2 cm -45 0.5 1/40 0.025 20 20/800 100 D 1 cm -50 0.4 0.4 M 70 3 p J# 1 125 D 0.8 cm -55 0.3 1/50 0.02 15 20/1000 Profound Low Vision Formulas used: 1/M X m = m / M = V (visual acuity) (B) M X D = M x 1/m = 1/V (magnification need) (C) Size credit + Distance credit = Acuity score (D) See text for discussion and explanation.
From: David R Tribble on 11 Jun 2010 14:09 WM wrote: >> How would you get to an infinite number of steps when each step has >> another finite number? > David R Tribble wrote: >> If each step is followed by another finite number step, how would >> you stop at any finite step? > WM wrote: > It is not necessary to stop somewhere in order to remain in the finite > domain. If you don't stop at any finite step, how can the list be incomplete?
From: Virgil on 11 Jun 2010 16:48
In article <c34d244c-dd51-4470-b6e6-82aa2920efaa(a)x27g2000yqb.googlegroups.com>, WM <mueckenh(a)rz.fh-augsburg.de> wrote: > On 11 Jun., 08:03, Virgil <Vir...(a)home.esc> wrote: > > > > My proof does not show which line is left. > > > > It also does not show that any line is left. > > Sorry, but you seem unwilling or unable to understand my proof. I do not find it to be a proof. > > > > > But it shows that finished > > > infinity is a non-mathematical notion. > > > > On the contrary, what can be defined cannot be barred from mathematical > > consideration, and "finished" infinity can be and has been defined. > > To be defined means to be called by a shorter name. To have a name > does not prove existence of the named. Think of several Gods which > have ceased to have believers. > > > > > Of course it is always the last > > > line that is left, and it is impossible to get rid of a last line > > > > Except that the process requires passing by every line so that there > > cannot be a last one. In order to pass any line, there must have already been a successor line in existence to pass to, so one can pass from one line to another line , but never pass from one line to no line. > > > > So if WM finds a last line, WM is talking of a different process. > > No I am looking at it from another position. > If all lines are there, all can be considered and removed. Only by completion of the infinite process. > That is the one side. > If no line is removed before the next is written, then not all can be > removed. That presumes that the entire infinite process cannot be completed, so cannot be used to prove that it cannot be completed. > > In case of finished infinity both statements must be true. But not simultaneously. One of them is true only during the process, and the other only after the process has stopped, so they need not be simultaneously true, and thus there is no conflict. |