Sentence examples for For this note from inspiring English sources

For this, note that if a, b are two nonnegative real numbers, then ( a + b ) 3 ≤ 4 ( a 3 + b 3 ) and a + b 3 ≤ a 3 + b 3.

For this note we assume the (X i,Y i )'s and (({C^{x}_{i}},{C^{y}_{i}}))'s are absolutely continuous and are also pairwise independent from each other.

For this note that begin{aligned} 2gamma _1 (J =gamma _1 (gamma _1 (J))=gamma _1 (JS =gamma _1 (J S=JS^2=J end{aligned}Since (2gamma _1) pro-generates (mathrm{Gal} (mathbb {L})) it follows that (Jin mathbf{G}(mathbb {L})) as desired.

For this, note that X can be equipped with the partial order ⪯ given by begin{aligned} &x, yin X,quad xpreceq y &quadLongleftrightarrowquad bigl( x t)leq y(t) forall tin[0, K] mbox{ and } | x|, | y|leq1 bigr) mbox{ or } x t)=y(t) forall t in[0, K]. end{aligned} (35).

— Gowiththeflow, Stamford, Conn .A. Thank you for this note.

"My reason for this note is that I remember reading a couple years ago that the average life span for professional football players is way, way shorter than just about any other profession".

"Everything else in our society is being squeezed and yet they have almost carte blanche for this," noted Greg Mitchell of the Nation on GRITtv this week.

Matt Yglesias chides Mr Biden for this, noting that borrowing at the time was quite sensible:[D]uring the Bush years, we had low inflation, low interest rates, and plenty of private investment.

Interviews were audiotaped and transcribed, or where recording was not possible (eg, because consent was not given for this) notes were taken and written up immediately.

Thank you for considering this note".

I said, "Mom, you're great for writing this note".