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There is no strangeness of zero. It is very natural. You use it to count objects. 0,1,2, .. they have a good physical model: number of stones. It's just the tea
by bmacho 2y ago
There is no strangeness of zero. It is very natural. You use it to count objects. 0,1,2, .. they have a good physical model: number of stones. It's just the teachers that insist on confusing kids. Also they are commonly called as 'natural numbers'. (Acknowledging the fact, that how they are called can't be a basis of an argument.)
Negative numbers however. They have no good physical models, at least that I know of. They are mostly just a tool to make accounting easier, or to denote one out of 2, indistinguishable cases (direction on the axis x, direction of angular velocity, electric charge). But the teachers don't insist confusing the kids with them.
- saurik 2y ago(FWIW, the "natural numbers" in fact does not include 0: if you include 0 you get the "whole numbers". I otherwise agree with you that 0 isn't at all strange.)
- 4ad 2y agoThe definition of natural numbers used in any sort of formalized mathematics includes zero. Without zero, you don't have induction (and ℕ wouldn't form a monoid).
- scapp 2y agoNothing wrong with starting at 1 for induction, but yes, having an additive monoid is nice (still get a multiplicative monoid with N*)
- bmacho 2y agoI did not know that "whole numbers" refer to nonnegative integers too. > The whole numbers were synonymous with the integers up until the early 1950s. In the late 1950s, as part of the New Math movement, American elementary school teachers began teaching that whole numbers referred to the natural numbers, excluding negative numbers, while integer included the negative numbers. The whole numbers remain ambiguous to the present day. https://en.wikipedia.org/wiki/Integer https://en.wikipedia.org/wiki/Integer > In mathematics, the natural numbers are the numbers 0, 1, 2, 3, and so on, possibly excluding 0. Some start counting with 0, defining the natural numbers as the non-negative integers 0, 1, 2, 3, ..., while others start with 1, defining them as the positive integers 1, 2, 3, ... . Some authors acknowledge both definitions whenever convenient. Sometimes, the whole numbers are the natural numbers plus zero. In other cases, the whole numbers refer to all of the integers, including negative integers. The counting numbers are another term for the natural numbers, particularly in primary school education, and are ambiguous as well although typically start at 1. https://en.wikipedia.org/wiki/Natural_number https://en.wikipedia.org/wiki/Natural_number What a shame.
- messe 2y agoIt's dependent on your choice of definition. Most include it.
- 8bitsrule 2y agoWhen I go to make a cake and need another cup of sugar, I have zero sugar. When I borrow a cup from the neighbor, and owe them one, I have -1 cups of sugar. Naturally.
- 4ad 2y agoYeah, in many ways the concept of a group is far more natural to us than the concept of natural numbers. I don't know why people make such a big deal of this, and why it's so badly explained in school.
- deleted 2y ago[deleted]
- ForOldHack 2y agoBrilliantly. This sentence no verb. Self referentially.
- hgomersall 2y agoYou get a long way if you start from geometry, the numbers just being written representation of geometric constructs. The numberline is one such geometric construct that can be interpreted easily with the reals (distance along the line from the origin in some direction). Complex numbers can then be considered an algebra representing rotations and translations in a plane. The various geometric algebras map to more geometric constructs again.