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 <aaloks...@gmail.com>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 <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 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.
>>
>
>  --
> 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.
>

-- 
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.

Reply via email to