On 27/02/2013 10:12 PM, Virgil wrote: > In article <R8AXs.345282$pV4.85998@newsfe21.iad>, > Nam Nguyen <namducnguyen@shaw.ca> wrote: > >> On 26/02/2013 2:47 PM, Virgil wrote: >>> In article <pk_Ws.104635$O02.20123@newsfe18.iad>, >>> Nam Nguyen <namducnguyen@shaw.ca> wrote: >>> >>>> On 26/02/2013 1:16 AM, Virgil wrote: >>>>> In article <m%XWs.20125$mC2.392@newsfe29.iad>, >>>>> Nam Nguyen <namducnguyen@shaw.ca> wrote: >>>>> >>>>>> On 25/02/2013 10:25 PM, Virgil wrote: >>>>>>> In article <SDWWs.99982$Hq1.27823@newsfe23.iad>, >>>>> >>>>>>> Since I said "not always", any such situation shows I am right. >>>>>> >>>>>> I think you misunderstood my point: >>>>>> >>>>>> In the context of language structure truth verification, >>>>>> your original statement would _always_ fail: because for >>>>>> Ex[P(x)] to be true, P(x0) must be true for some _example_ x0. >>>>> >>>>> To know that something must be true for some x0, it need not be known >>>>> for which x0 it is true, only that it is true for SOME x0. Which was my >>>>> original point! >>>> >>>> Then, can you construct a _language structure_ that would illustrate >>>> your point? >>> >>> It is well known that there is an infinite decimal, >>> x0, such that x0^2 = 2, but it is not known for which infinite decimal, >>> x0, it is true. >> >> Could you show me a language structure in which there's such an infinite >> decimal? > > The set of all functions from |N = {0,1,2,3,...} to {0,1,2,...,9} with > each f interpreted as Sum _(i in |N) f(i)/10^1, defines such a > structure..
That doesn't look like a structure to me. Could you put all what you've said above into a form using the notations of a structure?
-- ---------------------------------------------------- There is no remainder in the mathematics of infinity.
