The phrase "equivalent to the statement" is grammatically correct and can be used in written English.
It means that the part of the sentence being referred to has the same meaning as the statement being compared to. Example: "In the sentence, 'I cannot attend the meeting,' the phrase 'I cannot' is equivalent to the statement 'I am unable to'."
This is equivalent to the statement that the curve representing the transport numbers as a function of composition crosses the diagonal ("inversion point").
And mathematically, the statement that it's even is equivalent to the statement that if we replace the time argument by its negative, the function itself doesn't change.
In particular, Reinhart-Rogoff continue, to this day, to insinuate that the statement that "countries with debt above 90 percent of GDP tend to have slower growth than those with debt below 90 percent of GDP" — which is true, somewhat — is equivalent to the statement that there is a threshold at 90 percent at which bad things happen.
The celebrated Riemann hypothesis is equivalent to the statement that Ξ ( z ) has only real zeros.
This is equivalent to the statement that any sequence x = ( x n ) of points in E has a convergent subsequence whose limit is in E.
It is equivalent to the statement that in L 1, ({lim }_{nrightarrow infty }mathbb {E}[|Z_{n+1}-E_{n}|] = 0) which implies E[|Z ∞ −E ∞ |]=0.
Standard logic includes the "distributive" law, by which a statement of the form "X and either Y or Z" is equivalent to the corresponding statement of the form "Either X and Y or X and Z".
On this view, the sentence "Venus is the morning star" is logically equivalent to the complex statement "(i) There is a morning star, (ii) there is at most one morning star, and (iii) if anything is a morning star, then it is Venus".
Taking into account the expressions of and, condition is equivalent to the following statement.
It is equivalent to the following statement: (S5′) If x n → 0 and c ≻ 0, then x n ≺ c for all but finitely many n.
Finally, Theorem 1.1 is equivalent to the following statement which modifies a problem of Oppenheim (a problem of Oppenheim for circular functions can be found in [20, 27 29]).
