the infinity of not counting?

In my simple and/or simplistic mind, the sign of infinity denotes “that which we can not count”. In the infinitite set of odd numbers 1,3,5,7,9,11,13 etc – we can always add another number. Hence can not count all the numbers. The set might have the same number of elements as the even correspondant, however both infinite sets are uncountable in terms of Overall elements.
I take this as infinity’s seeming tight link of perhaps being time rather than space – however that might be some other discussion.
Back to counting.
In terms of uncountable, I take it there are at least 2 kinds of uncountables, that of the natural numbers and another of the real numbers.

In a sense, when checking numerical infinities, or checking infinities from a numerical point of view, we get a practice, or a process, of being non-countable. The countability in that sense is only a snapshot of time. If we count to 10 and pick up 8 as a relevant number for 4 + 4 = ? then we have a snapshot of time. We say the 8 in the continuum of even numbers is what we are interested at the moment.
At the moment is the clue for the time snapshot. A freezing in time.

Then we have another view of this. If indeed we are talking of time snapshots, then perhaps infinity or infinities are the elements that tend to be refred to as qualities rather than quanitities?

The quality is more personal, un countable. The 1st kiss, the last dance, the smile from your child, the feel of the wind, the scent of a lover, the redness of blue no one else has ever seen, the vibration of an intriguing thought, the need for desire, the pain of a realisation, the loss of time, etc. – we can do snapshots of these and Monetise. However, the monetisation of friendships, of time, of ReProducing a sense, or a memory of a sense – are precisely snapshots – not that which is indeed of the quality itself.

In that way, we might not actually have an easy way to share qualities. Not other than music notations, or indeed, words. However these are Communicative and hence guard-able ways for sharing. These are not ways from sharing need. Ways that might or might not communicate – but share none the less.

Going back to infinities, it seems to me, when considering the infinite sets of infinities and that these are non countable – that the nearest I can get to these in terms of senses which are not countable too – is via the vastness of qualities we can point out at. Indeed the times and practices we develop – as other animals – to do the qualities.
Therefore I seem to link between qualities and infinities. They are linked by being Uncountable. This might be a bit of an exaggeration though. A bit of a stretch. Because despite being in time, and uncountable, they are also different notions.
For example, the qualities we do, we are also happy to count, or to try and turn into countable snapshots. I do not not know that infinities like doing that, or that they lend themselves for that.
If there is a price on one’s sense of self worth, a price that might be a showing off by buying some latest tech gadget, or a price on friendships by telling facebook/google/tweeter/etc. one’s linked desires – then perhaps organic oriented qualities are not as infinite as the set of real numbers?

On the other hand, the set of real numbers does allow itself to have snapshots. It doesn’t break. we can take 0.000898978 + 0.9991 and do stuff with it right? Take it out of its infinite process and calculate X or Y. Does it mean all that set becomes uncountable?
If the snapshot of the infinite sense of morning sounds is X amount of coins – does it mean All the infinity of sensing morning sounds is the same X amount of coins too?