Anti-nominalism says there exist abstract mathematical objects, whereas platonism adds Independence, which says that mathematical objects are independent of intelligent agents and their language, thought, and practices.
There is an old adage which says there exist three types of lies; lies, damn lies and statistics.
That is to say, there exist real numbers (lambda _1le dots le lambda _r) and independent vectors (v_1,dots,v_r in V) (where (r = dim _{{mathbb C}} V))) such that begin{aligned} {fancyscript{H}}(v_i, v_i) = lambda _i {fancyscript{A}}(v_i,v_i). end{aligned}We can choose (v_i) such that ({fancyscript{A}}(v_i,v_i)=2) for all (i), as we assume from now on.
"I would say, there exist [in the world] immortal bacteria, immortal beings.
As we saw in section 1, to say that x is countable is just to say there exists such a bijection between x and the natural numbers; to say that x is uncountable is to say that there are no such bijections.
Brian Sykes, senior vice president at Beech Street Capital in Bethesda, Md., says there exists "one of the largest differentials between interest rates and cap rates" — or return on investment — " in history".
It says "there exists a substantial danger as a result that these debates will now not happen".
In Cook's piece, he says, "There exists no proof that censorship helps expedite a safe release, and there is no proof that accurate information about a victim harms him," suggesting the practice is to benefit employers, not kidnappees.
It said, "There exist serious questions about the conduct, true nature and objectives of the flotilla organizers, particularly I.H.H".
The new version, with no apologies for murdering the English language, said: "There exist conditions which might raise uncertainties about Sharp being an assumed going concern.
That is to say, there exist constants (d_{i}< 1), (i=1, ldots, l), such that frac{d r_{i}(t)}{dt }leq d_{i},quad i=1,2,ldots,l.
