is generally used as "such that", as in "under the condition that", often used interchangebly with
. That would make the first statement read "for all positive integers a, under the condition that b is a positive integer, such that b = a^3". However this makes no definition of b (and little sense), AND would be very strange since : is being used for such that later in the expression, which leads me to;
In this context I find it more likely this is a cursed "there exists" (should be
). That produces what I think is intended, "for all positive integers a, there exists a positive integer of b, such that b = a^3".
Rarely
is used as "an element of" (
) in the other direction - but that is nonsense here.
May this be a warning to notate well and unambigously.
