I was refering to "ordinal number" as explained in the wiktionary:"First, 
second and third are the ordinal numbers corresponding to one, two and three". 
That is not my invention. The ordinal fraction is my invention.

 

    Den 17:56 torsdag den 31. maj 2018 skrev 'Bo Jacoby' via Chat 
<c...@jsoftware.com>:
 

 "My decade, like the one of most others, start at 2010". Let's agree that each 
decade (or decennium) is ten years long. The first decennium starts at the 
first year and includes the tenth year. So the  n'th  decennium starts at the 
(1+10*(n-1))th year. The two hundred and second decennium starts at the 
(1+10*(202-1))th year, which is the two thousand and eleventh year, not the two 
thousand and tenth year.
The convention of using a period instead of "th" (4. means fourth) may not be 
common in English?
I completely agree that 0-origin is standard for cardinal numbers, and that 
ordinal numbers do not occur in J. 
 

    Den 15:57 torsdag den 31. maj 2018 skrev 'Bo Jacoby' via Chat 
<c...@jsoftware.com>:
 

 "If someone is 8 years old, she is in her 9th year, I would say. And what do 
you say?" I agree. The number of years that have passed is 8, and this year is 
her 9th. Christ is 2017 years old in this year 2018.  

    Den 15:50 torsdag den 31. maj 2018 skrev 'Bo Jacoby' via Chat 
<c...@jsoftware.com>:
 

    (4#10)&#:&.<:2018 
3 1 2 8
The (cardinal) number of years passed before the arrival of year number 2018 is 
2017, which is 2 millenia, 0 centuries, 1 decenium and 7 years. So the ordinal 
numbers are: third millenium, first century, second decenium, eighth year.
 

    Den 13:55 torsdag den 31. maj 2018 skrev R.E. Boss <r.e.b...@outlook.com>:
 

 > -----Original Message-----
> From: Chat <chat-boun...@forums.jsoftware.com> On Behalf Of 'Bo Jacoby'
> via Chat
> Sent: woensdag 30 mei 2018 21:26

> "2018 is the ninth year of the second decade etc"? No!The first decade
> consist of the years 1 2 3 4 5 6 7 8 9 10. 

Says who? 

>  The 202. decade consist of the
> years 2011 2012 2013 2014 2015 2016 2017 2018 2019 2020. 

That's your definition, dot included.
My decade, like the one of most others, start at 2010.

> So 2018 is the 8.
> year of the 202. decade, which is the 2. decade of the 21 century, which is 
> the
> 1. century of the 3. millenium.

Apart from 8 which should be a nine I agree on that.

If someone is 8 years old, she is in her 9th year, I would say. And what do you 
say?

I get the impression that your fractional ordinals depend on your definition of 
numbers followed by a dot.
OK, but we should be aware that you are off by 1, once and a while.


R.E. Boss
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