Numbers and Numerals

Date: 08/29/2002 at 17:29:48
From: Brent Yacobucci
Subject: Is 15/3 an integer?

I tutor high school mathematics, and a friend of mine threw this 
question at me. It has his 7th grade daughter, and me, stumped.

Is 15/3 an integer?  15/3 reduces to 5, which is certainly an integer.  
But is 15/3? Similarly, is square root(9) an integer?

I can't seem to find anything that says explicitly.

Thanks for the help.

Date: 08/29/2002 at 23:48:32
From: Doctor Peterson
Subject: Re: Is 15/3 an integer?

Hi, Brent.

The term "integer" is applied to numbers, not numerals 
(representations of numbers). So it doesn't matter that you are 
writing 5 in a fractional form as 15/3; the _number_ is still 5, 
and is an integer. And sqrt(9) is the integer 3.

Similarly, we can say that x+1 is an integer if x is an integer, even 
though "x+1" is an algebraic expression, not a numeral.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/