- #1

A.Magnus

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$\mathscr A_1$: If $x, y \in \mathbb R, x + y \in \mathbb R$ and if $x = w$ and $y = z$, then $x + y = w + z$.

$\mathscr M_1$: If $x, y \in \mathbb R, xy \in \mathbb R$ and if $x = w$ and $y = z$, then $xy = wz$.

To my untrained eyes, they do not mean anything at all. Could somebody therefore give an intuitive significance of the two properties, perhaps with examples - please. Are they about closure?

Thank you for your time and gracious helps. ~MA