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I want to write down the order of tuples $(a, b)$ with $a,b \in \{1,...,n\}$.

What is a good way to do so?

Right now I wrote: $(1,1),(1,2),\ldots,(1,n),(2,1),(2,2),\ldots,(2,n),(3,1),\ldots,(n,n)$

I'm unsure about the last part $(3,1),\ldots,(n,n)$.

Do you have any suggestions?

EDIT:

What I'm about is, how to write it down.

I definitely want to write down the order.

Less important is the question about the separator. I don't think, that < would be a good idea.

The more important question is, if $(3,1),\ldots,(n,n)$ makes clear, what is meant

user1
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1 Answers1

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Maybe you should have a look at Lexicographical order. Personally, I would not order such a set, but instead use the set notation $$A \times A := \left\{ (a,b) : a \in A, b \in A\right\}$$ where in your case $A := \{1,...,n\}$. A set without any specific structure does not have the notion of order.

To answer your question, I would write $$(1,1),...,(1,n),(2,1),...,(2,n),...,(n,1),...,(n,n)$$

TheGeekGreek
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