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```---- Original Message -----
From: "C. Brickner" <[log in to unmask]>
To: [log in to unmask]
Sent: Wednesday, December 18, 2013 11:21:18 AM
Subject: Re: Numbers, Counting, and Arithmetic

First off, multiplication is just a shortcut to addition, so that 5*3 is
the same as 5+5+5, "add 5 to itself 3 times," or "repeat 5 thrice." There's
no rule that says a language has to use a parallel shortcut (if there was,
we'd break it).
_______________________________

Math is definitely not my strong suit, but shouldn't that be "add 5 to itself 2 times"?  If I add 5 to itself once, the result is 10; if I add 5 to itself twice, the result is 15.  Some might say that the first addition is 5 itself, but if I add 5 to itself 0 times the result is 5 and I haven't really added anything.

More than willing to be enlightened!

Charlie
______________________________

On further thought: yes, 15 is 5 3 times: here's 5, here's 10, here's 15.  But is having 5 3 times the same as adding 5 3 times?  Here's 5. I add the first 5, here's 10.  I add the second 5, here's 15.  If I add a 3rd 5, the result is 20.  I can't add just 5.  Addition means 5 + x, in this case.  If x=5, then I get 5, 5 + x, 5 + 2x.  Two additions.

Charlie

Charlie
```