3 ms·

This wouldn't be a problem if people would stop thinking that the natural numbers start at 1.

by ionfish 16y ago

kenjackson 16y ago
That's probably the most popular way it is taught. And whole numbers starting at 0. Although oddly some people will learn in the complete opposite way. We could just throw away these short hands and just integers, positive integers, negative integers. Which actually led me to another potential reason for the confusion. Is zero positive or negative? OK, now is zero even or odd? I can imagine some just see zero with weird properties.
- ionfish 16y ago
  We could just throw away these short hands and just [use] integers, positive integers, negative integers. This depends on who you consider "we" to be. If we're talking about computer programmers, in most languages integers are all you get: natural numbers aren't available (although the Haskell community want them [1]). On the other hand, from the perspective of mathematics, the natural numbers are very different to the integers. For one thing, they're wellordered whereas the integers are not. Obviously a set-theoretic definition of the natural numbers (as the finite ordinals) will start at 0 since it's just identified with ø. Set-theoretic definitions of the integers are typically in terms of equivalence classes of pairs of natural numbers (or arbitrary elements from these equivalence classes if you want to work in ACA0) [2]. [1] http://hackage.haskell.org/trac/haskell-prime/wiki/Natural http://hackage.haskell.org/trac/haskell-prime/wiki/Natural [2] See SoSOA p.10 for details. http://www.math.psu.edu/simpson/sosoa/ http://www.math.psu.edu/simpson/sosoa/
- JadeNB 16y ago
  > Is zero positive or negative? OK, now is zero even or odd? I can imagine some just see zero with weird properties. I think that's the best explanation I've heard. Thanks! (Also you can't divide by it (although (http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/d...) …), so who knows what trickery it's up to?)

This wouldn't be a problem if people would stop thinking that the natural numbers start at 1.

by ionfish 16y ago

This wouldn't be a problem if people would stop thinking that the natural numbers start at 1.

That's probably the most popular way it is taught. And whole numbers starting at 0. Although oddly some people will learn in the complete opposite way. We could just throw away these short hands and just integers, positive integers, negative integers. Which actually led me to another potential reason for the confusion. Is zero positive or negative? OK, now is zero even or odd? I can imagine some just see zero with weird properties.

ionfish 16y ago
We could just throw away these short hands and just [use] integers, positive integers, negative integers. This depends on who you consider "we" to be. If we're talking about computer programmers, in most languages integers are all you get: natural numbers aren't available (although the Haskell community want them [1]). On the other hand, from the perspective of mathematics, the natural numbers are very different to the integers. For one thing, they're wellordered whereas the integers are not. Obviously a set-theoretic definition of the natural numbers (as the finite ordinals) will start at 0 since it's just identified with ø. Set-theoretic definitions of the integers are typically in terms of equivalence classes of pairs of natural numbers (or arbitrary elements from these equivalence classes if you want to work in ACA0) [2]. [1] http://hackage.haskell.org/trac/haskell-prime/wiki/Natural http://hackage.haskell.org/trac/haskell-prime/wiki/Natural [2] See SoSOA p.10 for details. http://www.math.psu.edu/simpson/sosoa/ http://www.math.psu.edu/simpson/sosoa/
JadeNB 16y ago
> Is zero positive or negative? OK, now is zero even or odd? I can imagine some just see zero with weird properties. I think that's the best explanation I've heard. Thanks! (Also you can't divide by it (although (http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/d...) …), so who knows what trickery it's up to?)