On 5/29/2012 4:38 PM, Aleksandr Lokshin wrote:

It is impossible to consider common properties of elements of aninfinite set since, as is known from psycology, a man can consider nomore than 7 objects simultaneously. Therefore consideration of suchobjects as a multitude of triangles seems to be impossible.Nevertheless we consider such multitudes and obtain results which seemto be true. The method we employ is comsideration of a very specific"*single but arbitrary*" object.Your remarkable objection that "*if two mathematicians consider twodifferent arbitrary objects they will obtain differentresults"* demonstrates that you are not a mathematician. Arbitraryelement is not an object, it is a mental but non-physical processwhich*enables one to do a physically impossible thing : to observe aninfinite set of objects simultaneously* considering then all theircommon properties at a single really existing object. Therefore twodifferent mathematicians will necessarily obtain the same result.

Hi Aleksandr,

`This makes mathematicians very special as they are able to escape`

`the bounds of resources that all non-mathematicians are subject to. How`

`would a mathematican prove to a layman that he truly has such powers?`

`Would they tend to beincorrigible`

`<http://www.merriam-webster.com/dictionary/incorrigible>? :-P`

On Wed, May 30, 2012 at 12:13 AM, Jesse Mazer <laserma...@gmail.com<mailto:laserma...@gmail.com>> wrote:On Tue, May 29, 2012 at 3:01 PM, Aleksandr Lokshin <aaloks...@gmail.com <mailto:aaloks...@gmail.com>> wrote: <</The notion of "choosing" isn't actually important--if a proof says something like "pick an arbitrary member of the set X, and you will find it obeys Y", this is equivalent to the statement "every member of the set X obeys Y"/>> No, the logical operator "every" contains the free will choice inside of it. I do insist that one cannot consider an infinite set of onjects simultaneously! Why do you think we can't do so in the way I suggested earlier, by considering common properties they are all defined to have, like the fact that each triangle consists of three straight edges joined at three vertices? If I construct a proof showing that, if I take some general properties as starting points, I can then derive some other general properties (like the fact that the angles add up to 180), where in such a proof have I considered any specific triangle? Do you think mathematicians actually have to pick specific examples (like a triangle with sides of specific lengths) in order to verify that a proof is correct? If they did choose specific examples, and only verified that it worked for those specific examples, how would they be able to achieve perfect confidence that it would be impossible to choose a *different* example that violated the rule? If you prove something is true for an "arbitrarily chosen member" of the set, this implies that in a scenario where someone other than you is doing the choosing, you should be totally confident in advance that the proof will apply to whatever choice they make. If the set they are choosing from is infinitely large, how could you have such perfect confidence prior to actually learning of their choice, without considering shared properties of "an infinite set of objects simultaneously"?--You received this message because you are subscribed to the GoogleGroups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com <mailto:everything-list@googlegroups.com>. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com <mailto:everything-list%2bunsubscr...@googlegroups.com>. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. --You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email toeverything-list+unsubscr...@googlegroups.com.For more options, visit this group athttp://groups.google.com/group/everything-list?hl=en.

-- Onward! Stephen "Nature, to be commanded, must be obeyed." ~ Francis Bacon -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to everything-list@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.