The following are variations in expressing "there exists a natural number $n$, such that $2T = n \cdot (n+1)$":
- $\exists n\in \mathbb {N},\; 2T = n \cdot (n+1)$
- $\exists n\in \mathbb {N}\; [2T = n \cdot (n+1)]$
- $\exists n\in \mathbb {N}\; {2T = n \cdot (n+1)}$
- $(\exists n\in \mathbb {N})\; 2T = n \cdot (n+1)$
- $\exists n\in \mathbb {N} \; : \; \{ 2T = n \cdot (n+1) \}$
- $(\exists n\in \mathbb {N}) \; (2T = n \cdot (n+1) )$
- etc
My question is: what is the official, or recommended, notation?
Does the answer depend on UK-USA or other traditions?
I have seen variations in many respected courses and textbooks.
Attached is Pro Keith Devlin's usage from his "Introduction to Mathematical Thinking" course - you can see he uses plenty of round and square brackets - but not colon which I had always used for "such that".
This is a related question but doesn't answer this question which asks for official / recommended / tradition: How do commas and brackets affect the meaning of quantifiers?