[Tutor] Picking Nits in "Learning to Program"

Alan Gauld alan.gauld at btinternet.com
Sat Feb 17 02:48:53 CET 2007

"Carroll, Barry" <Barry.Carroll at psc.com> wrote

> "Real Numbers".  The first sentence, "These are fractions" is 
> technically incorrect, but incomplete.  

Yep, I thought I'd changed that following a discussion 
with Dick Moores about the same section.

> While it's true that fractions (i.e. rational numbers) 

But here we come to an interesting divergence of opinion. 
You see, in UK Math classes fractions cover more than 
the rational numbers. A fraction is any number which is 
not a whole number(*). That's their definition in English (here) 
too. Of course that still makes my Real numbers wrong 
since, as you say, Reals include both whole numbers and 

(*) Thus we have decimal fractions...Blood fractions, 
atomic fractions etc etc...

> real numbers that cannot be expressed as a ratio of 
> two integers.  Hence the name "Irrational Numbers".  

I prefer rational and irrational as definitions because they 
mean the same both sides of the pond!

> "Fractions are examples of real numbers."  

And that's almost what I thought I'd said....

It seems I didn't upload the changed version. 
It now says of Reals: 'These include fractions'

I'll get the changed version uploaded over the weekend.
I'm happy for the nitpicking, because I do try to be very 
careful about my terminology, because as you say it is 
extremely important to be precise in programming. 
Occasionally we get these minor trans-Atlantic glitches 
but usually it's consistent :-)

Alan Gauld
Author of the Learn to Program web site

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