So -4 × 2 = -8 is easily grasped as adding -4 twice (-4 + -4 = -8), negative numbers simply being a different kind of number). — Agent Smith
However, from the books I read -4 × -2 = 8 is rather difficult to comprehend intuitively. What does adding -4 negative two times mean? It's just a pattern that's all and nothing in our everyday experiences can be used to convey the meaning of this particular calculation to children and adults alike. — Agent Smith
Most interesting. — Ms. Marple
The first culture to do math with negative numbers was the Chinese and they didn't have the concept of 0. I wonder what their definition of negative numbers was — Agent Smith
That is to say -1 isn't 1 with - sign, -1 is a completely distinct entity from +1. — Jerry
Euler, in the latter half of the 18th century still believed negative numbers were greater than infinity. — jgill
Actually, the Hindus about 628 introduced negative numbers to represent debts. Positive numbers represented assets. Euler, in the latter half of the 18th century still believed negative numbers were greater than infinity.
(I can't wait to see all the action when you guys move on to FRACTIONS :scream: ) — jgill
Can I ask you where you got this from? I know Euler played fast and loose with infinite series, but I can only find this bit about negative numbers mentioned on an obscure Wikipedia comments page. Since Euler is one of the greatest minds mathematics has ever seen, this seems like an odd mistake. — Real Gone Cat
As someone mentioned elsewhere, negative numbers are typically built within set theory as equivalence classes of pairs of natural numbers, so they are very much one level up.
So -2 := { (2,4), (3,5), (4,6),...}.
It's also possible to declare that every number in a given system has an additive inverse. — Pie
It's not that Euler was stupid, but maybe the reverse. — Pie
For me, these kind of constructions raise a lot of questions about the sort of ontology of mathematical objects — Jerry
We are relatively stupid beings, but (paradoxically) we are intelligent enough todiscoverstumble upon interesting things we can't understand — alan1000
Euler, in the latter half of the 18th century still believed negative numbers were greater than infinity. — jgill
Can I ask you where you got this from? — Real Gone Cat
Is there no insight to be gained by understanding why the idea of a negative eluded such minds for so long? — Jerry
(I can't wait to see all the action when you guys move on to FRACTIONS :scream: ) — jgill
And yet, when introducing children to the concept of negatives, we use a line to wit the number line. — Agent Smith
In one sense, geometry's anti-negative numbers and in another sense it is pro-negative numbers!
What up with that? Anyone have any ideas? — Agent Smith
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