```Date: Mar 13, 2013 2:19 PM
Author: fom
Subject: Re: Matheology § 222 Back to the root<br> s

On 3/13/2013 12:33 PM, WM wrote:> On 13 Mrz., 17:59, William Hughes <wpihug...@gmail.com> wrote:>> On Mar 13, 5:37 pm, WM <mueck...@rz.fh-augsburg.de> wrote:>>>>> On 13 Mrz., 13:19, William Hughes <wpihug...@gmail.com> wrote:>>>> <snip>>>>>>> If you wish to contest this, use my words not>>>> yours  (e.g.  I have never said "The list contains more>>>> numbers than fit into a single line",  I have said>>>> "There is no line in the list which contains every>>>> number in the list".)>>>>> Correct. The list has more numbers than a single line has. Since every>>> number that is in the list, must be in at least one line, this implies>>> that the numbers are in more than one line.>>>> To be precise, a set of lines, say K, that contains all the numbers>> contains at least two lines.>> In actual infinity, this is not avoidable.> We note: At least two lines belong to the set that contains all> numbers. We call these lines necessary lines.> So the set of necessary lines is not empty.>>>    However, this does *not* imply that>> there are two numbers that are not in a single line.>> Why then should two lines be necessary?> One being the substitute in case the other falls ill?>>> Nor does it imply that there is a necessary line in K.>> If there is not one necessary line, then there are two or more> required.> Proof: If you remove all lines from the list, then there remains no> line and no number.>>> Note that a sufficient set does not imply a necessary line>> even in potential infinity.  There is no line that is needed>> to make L have an unfindable last line.>> So you believe that there can remain all numbers in the list after> removing all lines? That is a remarkable claim. I would not accept it> in mathematics.>> Note in actual infinity it makes sense to talk about all lines and to> remove all lines.I think this is just a difference of interpretationconcerning "necessary".To borrow from linear algebra, you are describingsomething that might be more along the lines ofa "spanning set".  Any particular lines are notnecessary, but whenever one speaks of the possibilityof given lines containing all the numbers, thecount of those lines would necessarily have anon-zero value greater than one because ofpartiality.
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