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Yet life arose, and, over millions of years, it came to exist in infinite numbers and endless variety.
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The language itself can exist in an infinite number of states but its intent generally clusters around simple outcomes (I'll take the deal or reject it).
-- big bangs probably happen all the time, perhaps in infinite numbers.
In such a situation, there exist an infinite number of dynamic flux combinations v(t k ) that satisfy X ˙ m t k = S v t k.
In accordance with this, other civilizations, including more "successful" ones, should exist an infinite number of times on the "preceding" and the "following" pages of the Book of the Universe.
"Other civilizations, perhaps more successful ones, may exist an infinite number of times on the preceding and following pages of the Book of the Universe," Sakharov wrote in his Nobel Prize lecture.
Greek mathematician Euclid (flourished c. 300 bce) gave the oldest known proof that there exist an infinite number of primes, and he conjectured that there are an infinite number of twin primes.
Under a fixed, there exist an infinite number of threshold pairs achieving a fixed.
The axiom of infinity in effect states that there exists an infinite number of objects.
For instance, in case of 1D GPE there exists an infinite number of local conserved charges, which can be explicitly calculated using Zakharov Shabat construction [19].
He also argued that the thesis of the Aristotelian philosophers that there exists an infinite number of causes and effects, which have order and gradation, was impossible.
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