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Set $\theta = \{((x^2,y),(y,2x,x-y)): x,y \in \mathbb{Z}\}$ a function? What is domain, range, codomain?

Domain: set of $(x^2,y)$ for $x,y \in \mathbb{Z}$

Range: set of $(y,2x,x-y)$ for $x,y \in\mathbb{Z}$ and the codomain is the same as the range.

This is a function because each set is "unique" from the previous set.

If I did this all correctly?

halrankard
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EM4
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    If x = (-1), then you get the same first-coordinate value for an element of $\theta$ as you would get for x = 1, but the second-coordinate values are different since (2(-1)) isn't equal to (21), so $\theta$ isn't single-valued, so $\theta$ isn't a function. – Ren Eh Daycart Jul 27 '20 at 18:07
  • @RenEhDaycart What about the third coordinate? – CiaPan Jul 27 '20 at 19:00

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Note that $$((1^2,0),(0,2 \cdot 1,1-0)) = ((1,0),(0,2,1))$$ and $$(((-1)^2,0),(0,2 \cdot (-1),-1-0)) = ((1,0),(0,-2,-1))$$ both belongs to $\theta$.

azif00
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