Comment author:Barry
03 December 2007 07:04:12AM
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I recall my music teacher once put a quote on the board which I shall now adjust to the problem: Take 2 piles of sand and 2 more piles of sand and add them together. What do you get? 1 or more piles of sand.

Not directly applicable to the general understanding of integers, but amusing to me. You could also do similar quibbles with musical tones or beats.

Then again it could all be rubbish...for I don't think I could argue any of the points argued so far, though I do find my attempt at understanding it enjoyable if not complete.

Comment author:bigjeff5
03 March 2011 07:54:41PM
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Yet if you counted the grains of sand, you would have as much sand as is contained in four piles of sand - 2+2=4.

This is the same as saying when I add 2+2 and get 4, I start with two numbers and only get one number. It's true, but you've fooled yourself into believing this is some profound mathematical truth (and in a sense it is, but not the way you originally thought), when in fact it was so obvious to anybody who wasn't trying to fool themselves that it did not need pointing out.

This is also the same as starting with two groups of two apples, adding them together, and getting one group of four apples. I'm not disappointed by this result. In fact, the very reason I have four apples is because I have merged two groups of two apples into a single group. The result of this merger is four apples.

## Comments (390)

OldI recall my music teacher once put a quote on the board which I shall now adjust to the problem: Take 2 piles of sand and 2 more piles of sand and add them together. What do you get? 1 or more piles of sand.

Not directly applicable to the general understanding of integers, but amusing to me. You could also do similar quibbles with musical tones or beats.

Then again it could all be rubbish...for I don't think I could argue any of the points argued so far, though I do find my attempt at understanding it enjoyable if not complete.

Yet if you counted the grains of sand, you would have as much sand as is contained in four piles of sand - 2+2=4.

This is the same as saying when I add 2+2 and get 4, I start with two numbers and only get one number. It's true, but you've fooled yourself into believing this is some profound mathematical truth (and in a sense it is, but not the way you originally thought), when in fact it was so obvious to anybody who wasn't trying to fool themselves that it did not need pointing out.

This is also the same as starting with two groups of two apples, adding them together, and getting one group of four apples. I'm not disappointed by this result. In fact, the very reason I have four apples is because I have merged two groups of two apples into a single group. The result of this merger is four apples.

Could you please define a "pile"? :3

A pile is a collection of 0 or more grains of sand.