We included a convergence proof in that paper, but only proved rates of convergence in some greatly simplified situations.
This strategy clearly shows that Brouwer's operative explanation of the meaning of A → B was a version of clause (H3) of the Proof Interpretation as formulated in the Introduction, if we understand "proof" in that clause as "demonstration".
Results from the experiment indicate that students meaningfully learned about aspects of both algebra and proof in that they produced algebraic proofs involving multiple variables, based on conjectures they themselves generated.
If you look at smaller and smaller scales, pixels and voxels can be no smaller, there's a minimum pixel size of the world… There's no real proof in that, but it's interesting food for thought".
On a separate track, the field continues toward building on the RV144 trial in Thailand, which in 2009 provided the first proof in that a vaccine can, indeed, prevent infection.
As compared to the cancer field, the one initiating clinical study providing proof-in-principle that fibrosis can be reversed in patients is still lacking.
"That is proof in itself that change is possible," McPhatter went on to tell a crowd gathered outside of New York's City Hall to commemorate Dr. Martin Luther King on what would have been the icon's 87th birthday. .
"We had proof in letters that Brooke Astor felt she wanted to sell that painting at one time," Ms. Fernandez said.
In Vine's case, it was Ed Miliband's kitchen that was deemed wanting in her column – proof, in fact, that he and his wife are "aliens".
"The fact that over 70 new drugs have been detected in the last year is proof in itself that drug policies need to adapt to changing drug markets".
And ultimately proof, in fact, that it did not.
