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Rasalhague

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**Meaning of "we require that"**

Wikipedia: Dynamical system:

In particular, for S to be Φ-invariant,we require thatI(x) = T for all x in S. That is, the flow through x should be defined for all time for every element of S.

Does this mean

*(1) If I(x) = T for all x in S, then S is Φ-invariant?*

(2) If S is Φ-invariant, then I(x) = T for all x in S?

(3) If and only if S is Φ-invariant, then I(x) = T for all x in S?

(I.e. The above definition of Φ-invariance of S is equivalent to the the requirement that I(x) = T for all x in S.)

(2) If S is Φ-invariant, then I(x) = T for all x in S?

(3) If and only if S is Φ-invariant, then I(x) = T for all x in S?

(I.e. The above definition of Φ-invariance of S is equivalent to the the requirement that I(x) = T for all x in S.)

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