So you believe that the set of all numbers divisible by two is not the set of all even numbers?
On Tue, May 29, 2012 at 1:38 PM, Aleksandr Lokshin <[email protected]>wrote: > 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 <[email protected]>wrote: > >> >> >> On Tue, May 29, 2012 at 3:01 PM, Aleksandr Lokshin >> <[email protected]>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 [email protected]. >> To unsubscribe from this group, send email to >> [email protected]. >> 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 protected]. > To unsubscribe from this group, send email to > [email protected]. > 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 protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
