Less vs Fewer

I used to be oblivious to this, but now I know, misuse increasingly sticks out like a sore thumb:

  • “Less” is for an amount of bulk stuff you’re not counting in discrete units – less water, less food, less stock
  • “Fewer” is for discrete, countable things – fewer drinks, fewer meals, fewer items at a checkout

So if the sign at your checkout says “10 items or less”, it’s just wrong.  Silly sign.

0.9 repeater = 1 exactly

This blew my mind.  If you asked me a few days ago, I’d have said that 0.999999 (with 9’s repeating to infinity) could never exactly equal 1, since it would always be that little bit less than one.  Sure, it would tend towards one asymptotically, but it would never quite get there.  But here’s a proof someone told me to show that it does actually equal precisely one:

1/9 = 0.111111 (with 1s repeating to infinity)

Multiplying both sides by 9 gives:

1 = 0.999999 (with 9s repeating to infinity)

This seems to make much and little sense, simultaneously!  I guess infinity means an awful lot of nines.  My brain hurts.