fergusrush wrote:By "feel" I was referring to intuition, that sense that something is a particular way because similar things are that particular way.

Yes, I understood what you meant. And my reply still stands.

fergusrush wrote:The infinite series is merely the mathematical equivalent to the word "infinity" itself: the word allows us to name that which has not and cannot be achieved in the material universe but surely exists (yes, I know this leads to another conversation entirely!), while the series allows us to measure that which is endless.

But do you not realize that "infinity" does not exist period, not merely in the physical, but even the concept is an error (produced by those who rely too much on the intuition). That which is infinite has no end. The concept of "infinity" is the concept of "The greatest point of that which has no greatest point" or "the end of endlessness" - an

oxymoron.

in·fin·i·ty

inˈfinədē/

noun

1.

the state or quality of being infinite.

"the infinity of space"

synonyms: endlessness, infinitude, infiniteness, boundlessness, limitlessness; More

2.

MATHEMATICS

a number greater than any assignable quantity or countable number (symbol ∞).

The "state of being infinite" is called "infinite", not called "infinity". But they had to make up something because people keep using the word as if the noun actually made sense. The word "infinite" is the adjective, not "infinity".

And then in math, obviously there is no number greater than any number that can be applied to an infinite series. That is the oxymoron in the common usage.

fergusrush wrote:Mathematics is the art of measurement, after all.

More or less true. Mathematics is

logic as applied to quantities.

Science is more the art of measurement.

fergusrush wrote:The infinite series is not smaller because "there is ALWAYS a smaller amount to be added" because THAT is not what the infinite series IS. That kind of thinking implies a truncation: one has looked NOT at the series as a whole but only up to a point...and found it wanting. Just as we say "infinity" to name something endless, the series must be seen as a single name for the process.

This is the part that is interesting and again, seemingly self-contradictory.

"The infinite series is not smaller because "there is ALWAYS a smaller amount to be added" because THAT is not what the infinite series IS."

It's hard to be certain, but I think you're stating that

an infinite series is not a series that always has more to add. That would be an error in definition on your part. The ellipsis, "..." specifically means "infinitely/endlessly extended", having no end or destination. The word "infinity" implies an final destination.

"That kind of thinking implies a truncation:"

That is the contrary part. Thinking that something is endless, is not implying a truncation at all, quite the reverse. Thinking that infinity exists, even as a valid concept, is implying a truncation. It implies that there is a point "at infinity", yet there is no "at infinity". Those who think that 1 = 0.999... are thinking in terms of "once the series reaches infinity, it will be equivalent to 1.0". But of course, there is no "infinity" to be reached.

They "truncate" the endless process.

"one has looked NOT at the series as a whole but only up to a point...and found it wanting."

One has looked at what the series states and found that there is no end and thus "found it wanting". The more simple minded imagines an end "at infinity" and thus sees it as a completed process. It is a common error of imagination.

"Just as we say "infinity" to name something endless,"

That part would be largely true, but more like "we say 'infinity' to name the destination of something endless". And that of course, is logically senseless, but

intuitively implies the greatest possible even though there is no "greatest possible".

"the series must be seen as a single name for the process."

An

ENDLESS process, yes.