The phrase "avoid contradiction with" is correct and usable in written English.
You can use it when discussing the need to ensure consistency or alignment between statements, ideas, or actions.
Example: "In order to maintain clarity in our communication, we must avoid contradiction with our previous statements."
Alternatives: "prevent inconsistency with" or "ensure alignment with".
So, for sufficiently small α > 0, we have ∏ j = 0 11 ( 2 2 + ( α + j ) 2 ) < 2 ⋅ 10 17 < ∏ j = 0 11 ( 1 + α + j ) 2. Hence, for these α, in order to avoid contradiction with the definition of ρ 12 , the inequality ρ 12 2 > 2 2 is necessary.
end{aligned} Letting (n to+infty), we get begin{aligned} Nbigl(x_{n},x^, tbigr) &= minbigl{ M bigl(x_{n},x^,tbigr),M x_{n}, Tx_{n}t),t bigl(x^,Tx^,tbigr)bigr} &toMinbigl{ 1,1,Mbigl(x^,Tx^,tbigr bigrgr} &tominbigl{^,Tx^, tbigr) end{aligned} and so, to avoid contradiction with (phi(c)< c) for (c>0), we conclude that frac{1,1,Mbigl x^,Tx^}-1 = 0.
The trouble with this suggestion is that much of the detail of the Protagorean/Heracleitean position in 151 184 seems to be generated by Protagoras' desire to avoid contradiction.
But it has to make sense on some level -- preferably, musically -- or at least avoid contradictions.
The scenarios should be made internally consistent by avoiding contradictions (e.g., by combining political uncertainty with lower volatility).
To avoid a contradiction with Lemma 2.4, we get n h ( z ) + h ( z + c ) − h 1 ( z ) and ( n + 1 ) h ( z ) − h 1 ( z ) are constants.
Einstein points to Louis de Broglie's pilot wave investigations as a possible direction to pursue if one is looking for an account of individual processes that avoids a "contradiction with the postulate of relativity".
4 Boolean networks avoid such contradictions with sequential time steps (synchronous or asynchronous) for switching states in feedback systems.
The goal of the opponent is to trap the respondent into a contradiction and the goal of the respondent is to avoid the contradiction.
The introduction of the nuclear/extra-nuclear distinction allows us to avoid this contradiction.
Contemporary Fregeans, such as Boolos (1986-87), Wright (1983), and Anderson and Zalta (2004), have found ways to avoid the contradiction.
