Recent content by Sir_Deenicus

http://www.catb.org/~esr/jargon/html/story-of-mel.html"

I think the definition works, and I do not think it is meaningful to infer backwards. I think <x,y> => {{x}, {x,y}}. That when x = y, we have a singleton means that since all parameters are equal the choice of first is ambigious or trivial. Because {{x},{x,y}} is a definition and a convention...

On http://www.science.psu.edu/alert/Math10-2005.htm" . In one of the pictures you see a 2D projection (shadows) of a 3D projection of a 4D object.

I agree with all that! And can also truthfully say that I did not (fully) before this exchange. I have much to learn yet and wish I had already the knowledge so that a more interesting conversation would have been possible. I nonetheless do not think this a wasted endeavour since I at least...

But it is your word vs his... Nonetheless I have no knowledge of surreal numbers beyond that they have to do with something called Conway Games. However on hyperreals, your second point, point 2, is exactly what I have been arguing! Why am I still so certain of incompleteness of *R? I have 4...

Thanks, that one helped a lot. My knowledge of topology is pretty cursory and gotten from a CS angle. I am soon to undertake a proper math treatment on it and its algebraic counterpart however. On NSA however, I am more confident on, having read more (first Keisler, then numbers, then an...

Hurkyl your post is long and I was only able to skim but will read it more thorougly later. (it also got a bit disconnected as you went on :P). I have no problems with the internal sets agreeing, I see now that it is obvious. But I extended my issue not with them but to P(*R), which you later...

Lol :biggrin:, I am glad you think me so skilled but I am far from it. I am only 3 years older than your 17 by a few months and am a first year maths student in University. In fact, I too did not learn any mathematics in high school (no geometry or calculus, only algebra). I reaped the public...

I'll just get this out of the way now: 11.6 (although I could have by 5 but apparently I wasnt mature enough. Pheh)

Hurkyl, on further thought, I will accept that the sequence converges in *N not because the transfer principle allows that *R is complete but because a N statement True in N <--> True in *N. Otherwise as Matt clarified for me NA would not be so useful. But then again, the converse is not true...

Dont worry, the future is not doomed. Most of us with real interest tend to stay away from such trashy books and even have copies of books from those passed away 100 years gone!

Quoted for truth. :biggrin:

Okay. I will keep this in mind as I learn more NA. Thank you very much for your help and time, I truly do appreciate it.

Hurkyl, I am still not sure I agree with your use of the transfer principle. If for no other reason that in Keisler's book, he states that a completeness statement is not a real statement and thus not transferable over to *R. This creates a clash of confusion for me and I am more willing to...

First I'd like to apologize for being so dense. I always assumed that when you said that the difference is real, you meant real, exists instead of Real, the numbering system. The statement would have to be true since both numbers are in R since and R is subset... Yes. Thank you for your...