'Honest' Numbers

Date: 11/11/2002 at 18:27:19
From: Samantha Lee
Subject: "Honest" number

My teacher asked the class: What is the only "honest" number? Why?  

Please help me to answer these two questions. It would be most 
appreciated.

Date: 11/12/2002 at 01:41:28
From: Doctor Ian
Subject: Re: "Honest" number

Hi Samantha, 

It appears that some math teachers use the term 'honest' in this way:
Four is an 'honest' number because the name 'four' contains four
letters. By comparison, three would not be an 'honest' number because
the name 'three' contains five letters (too many), and five would not
be an 'honest' number because the name 'five' contains four letters
(too few). 

However, if this is supposed to be an attribute of the _number_, it's
not clear why it should depend only on spellings in English, and not
on spellings in other languages. For example, in Spanish, we have

  4  <-->  'cuatro'    (not honest)
  5  <-->  'cinco'     (honest)

and in Italian, we have

  3  <-->  'tre'       (honest)
  4  <-->  'quattro'   (not honest)

So this isn't really a mathematical concept at all, but a linquistic
one, which applies not to the _number_ four, but to the _word_ 'four'. 

I hope this helps.  

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