'Infinitesimal' in a sentence: Your chances of being in the wrong place at the wrong time are infinitesimal.
I agree with the first sentence, but not with the second. One particular English word — inifinitesimal — is a very frequently used word in the sort of English I read, and I would be amazed to see it misused in this way by a physicist or mathematician. But I presume O’Hagan is n...
We can hence paraphrase the latter sentence saying that the amplitude (of the derivatives) of these physical quantities is much larger than all the other (finite) quantities we can estimate in the system. However, this is a logical consequence of our lacking of interest to include in our ...
[/itex], in the context of what we're doing it is only a function of [itex]\alpha[/itex] being evaluated at [itex]x = x_0, y = y_0[/itex], thus the last sentence of your post is also a misinterpretation of what we're actually doing as those partials are never meant to...
In such a universe, any given mathematical statement (that is to say, a sentence with no free variables) is either true or false, with no intermediate truth value available. Similarly, any deterministic variable can take on only one specific value at a time." This makes se...