It is impossible to consider common properties of elements of an infinite set since, as is known from psycology, a man can consider no more than 7 objects simultaneously. Therefore consideration of such objects as a multitude of triangles seems to be impossible. Nevertheless we consider such multitudes and obtain results which seem to be true. The method we employ is comsideration of a very specific "*single but arbitrary*" object. Your remarkable objection that "*if two mathematicians consider two different arbitrary objects they will obtain different results"* demonstrates that you are not a mathematician. Arbitrary element is not an object, it is a mental but non-physical process which* enables one to do a physically impossible thing : to observe an infinite set of objects simultaneously* considering then all their common properties at a single really existing object. Therefore two different mathematicians will necessarily obtain the same result.
On Wed, May 30, 2012 at 12:13 AM, Jesse Mazer <laserma...@gmail.com> wrote: > > > On Tue, May 29, 2012 at 3:01 PM, Aleksandr Lokshin <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 Google Groups > "Everything List" group. > To post to this group, send email to firstname.lastname@example.org. > 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. > -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to email@example.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.