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MienTommy
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It means the Cartesian product ##\mathbb{N} \times \mathbb{N}##MienTommy said:What does the N^2 mean in this case? (Image below)
Yes.Does it mean, for all two pairs of natural numbers, a and b?
You just did, didn't you? What are non pair numbers? Or did you meanHow would I represent non pair numbers, i.e. how would I write "For integers k,l, and m such that k>1, l>2, m>k+l" all in one line?
If you remove the parenthesis, then one ##\mathbb{N}## is enough. There is a subtle difference between them: ##k,l,m \in \mathbb{N}## are simply three natural numbers, whereas ##(k,l,m) \in \mathbb{N}^3## is a ordered triplet. In most cases this doesn't really matter, but rigorously it's not the same. And of course one wouldn't actually write all conditions below each other since it's impractical. An alternative would be to write ##\forall_{k,l,m \in \mathbb{N}} \,\text{ with }\, k>1\,,\,l>2\,,\,m>k+l \;:\;## etc.MienTommy said:Yes that is what I meant. I wanted to know the symbol form. Would you add a such that symbol '|' after N×N×N? If I removed the parenthesis, ∀k,l,m∈N×N×N | k>1, l>2, m>k+l
Then would it mean the same thing?
##(1,2,3) \neq (2,3,1)## but ##1,2,3## are only three numbers.MienTommy said:I see. What is the difference between the ordered triplet and the other?
If A and B are sets A^B is the set of all maps of B into A. In your case 2 stands for a set with two elements, {1,2} for example.MienTommy said:What does the N^2 mean in this case? (Image below)
Does it mean, for all two pairs of natural numbers, a and b?
How would I represent non pair numbers, i.e. how would I write "For integers k,l, and m such that k>1, l>2, m>k+l" all in one line?
N^2 in the case of natural numbers refers to the square of a natural number, which is obtained by multiplying the number by itself. For example, N^2 of 3 would be 9, as 3 multiplied by itself equals 9.
In mathematical notation, N^2 is represented as N², where the small 2 above N indicates the exponent or power to which N is raised.
N^2 represents the square of a natural number, while 2N represents twice the value of a natural number. For example, N^2 of 4 is 16, while 2N of 4 is 8.
The square of a natural number N is equal to the product of N and itself. In other words, N^2 is the result of multiplying N by N.
N^2 is used in various scientific calculations, such as calculating areas and volumes. For example, the area of a square with side length N is given by N^2, and the volume of a cube with side length N is given by N^3.