obsrvr524 wrote:That author points out that people have had a lot of trouble understanding the issues of infinity

I'm sure that I'm not in a position to argue with Euler, Hewitt, Newton, Gödel, Robinson and probably hundreds of others

You seem to have trouble with it all just as the author of that article, Hermoso, admitted to having.

The author of that article I linked, and both you and I aren't in a position to argue with Euler, Hewitt, Newton, Gödel, Robinson and probably hundreds of others too. How about James?

The difference between his usage and the last 70 years of the number set being accepted to the extent that it has been seems striking to me, as does the logic behind his usage. You, James and I may not be world famous mathematicians, but does that mean we are equally amateurish? It's not without problems for each of us to argue the relative legitimacy of our arguments, and regardless even of the full potential that we each achieved at any given point during our respective lives, the standard of what James wrote on his blog some years ago is of the sort I used to play around with when I was a child. Having achieved top marks throughout my mathematical education, and maintaining significant interest and exposure to much higher levels over the decades since, I know there are at least some objective measurements to justify at least a higher level of amateur ability within myself - and I have no interest in overstating this subjectively, but I do have interest in criticising content that appears to me to be exhibiting lower levels of amateur ability, yet is gaining traction and influence over others who may be susceptible to mathematical sophistry due to their own standard being insufficient to see past it. Hell, I might be wrong, but I know there's plenty of reason for me to not be. I will put what I have out there, and you can take it or leave it, though I recommend you take at the very least a healthy amount of skepticism with you that you don't yet appear to be exhibiting.

obsrvr524 wrote:1) Do you have trouble with the idea that one infinite set can be known to be larger than another?

2) Do you find something specific, very specific, that you consider to be invalid reasoning or usage from James? Please exactly, precisely, quote an example of the error.

1) I have zero trouble with how people can think they understand one "infinite quantity" to be larger than another even though it's undefinable, using their intuitions about

finite quantities. The Hyperreals meet the transfer principle with respect to the Reals, but that does not make them equivalent - especially in how to treat their results.

For example, I have zero trouble with representing two infinite sums added together as twice the initial sum, particularly if it is a convergent series. However, to gain meaning from doing the same to divergent series is not without problems that need to be approached with due respect and caution. You can "represent bigger infinities", giving a semblence of size comparison between two or more, but this still makes no real-world sense as they both diverge forever and therefore never get to the point where they can be compared. Any specificity in constructing and comparing infinites is in their means of construction, not in the end itself - which you can only physically get to, by definition, if it's a finite value. Do

you have trouble accepting this logic?

2) I've been giving specifics all this time, in particular in

this post, which starts off with the most glaring contradiction so far:

obsrvr524 wrote:James addressed that issue nicely by first acknowledging what happens when you try to use "infinity" in maths. He explains it doesn't work. He explains that "infinity" is insufficiently defined for mathematical use.

metapointperspective.blogspot.com/2014/07/why-universe-exists.html wrote:Using a Cartesian system, there are 3/4 * Pi * infinity^6 points in the entire universe.

But I'm re-reading previous posts of mine as well and they too are specific, exact, precise and with quotes for reference - as you requested... Do

you have trouble accepting their logic?