[sangnoir]

Estimation is counting with error bars.

Frankly, most of what you consider counting in your comment needs error bars - ask anyone who operated an all-cash cash-register how frequently end-of-day reconciliation didn't match the actual cash in the drawer (to the nearest dollar.)

The following is a list from my personal experience - of presumably precisely countable things that didn't turn out to be the case: the number of computers owned by an fairly large regional business, the number of (virtual) servers operated by a moderately sized team, the number of batteries sold in a financial year by a battery company.

[shkkmo]

Counting is a subset of estimation, not a synonym.

If I estimated the number of quarters in a stack by weighing them, that would be different from estimating the number of quaters in a stack by counting them. Both methods of estimation have error bars.

The list you provide is of categories that don't have clear definitions. If you have a sufficiently clear definition for a category given your population, it has a precise count (though your counting methodologies will still be estimates.) If your definition is too fuzzy, then you don't actually have a countable set.

[throwaway290]

It's close enough to counting for the purposes of a magazine article like uuids are close enough to being unique for the purposes of programming.

[shkkmo]

The algorithm accuracy scales with the ratio of memory to set size so you don't actually know if it is "close enough" without an estimate of of the set size.

I think the headline is clickbaity and the article makes no effort to justify it's misuse of the wors 'counting'. The subheadline is far more accurate and doesn't use that many more words.

[Levitz]

I think I get your point completely, yet I'm not getting through.

Would you agree that 1+1=2? Or that pi is 3.14159...? These are mathematical truths, but quickly crumble in the real world. One apple plus one apple doesn't just equate to double the apple, no two apples are ever the same to begin with, there are no real perfect circles out there either, there is still value to those mathematical truths in that they make it evident that they are perfectly precise and that it is real world interaction which may bring error into the table.