assume axiom in a sentence
1) I do assume the axioms, and I do assume existence.
2) Or, does the objector assume the axioms as well.
3) Assuming the axiom of choice, addition of infinite cardinal numbers is easy.
4) Assuming the axiom of choice, multiplication of infinite cardinal numbers is also easy.
assume axiom example sentences5) The former result opened the door for mathematicians to assume the axiom of choice in their proofs.
6) Theorem: ( Assuming the axiom of countable choice) The union of countably many countable sets is countable.
7) Assuming the axiom of choice, it can be proved that the Dedekind notions correspond to the standard ones.
8) If we assume the axiom of choice, this space is much bigger than __FORMULA__ except in some trivial cases.
9) Assuming that axiom turns the axioms of infinity, power set, and choice (7 − 9 above) into theorems.
10) If someone can think of a denial, which does not assume the axioms, then I will reopen this part of the paper.
11) This result has had considerable consequences for working mathematicians, as it means that they can assume the axiom of choice when proving the Hahn-Banach theorem.
12) He also showed that neither the axiom of choice nor the continuum hypothesis can be disproved from the accepted axioms of set theory, assuming these axioms are consistent.
13) Assuming the axiom of choice and, given an infinite cardinal "π" and a non-zero cardinal μ, there exists a cardinal κ such that μ · κ = "π" if and only if μ ≤ "π".
14) There are important statements that, assuming the axioms of ZF but neither AC nor ¬AC, are equivalent to the axiom of choice.
example sentences with axiom15) Assuming the axiom of choice, the following are equivalent:
16) All the remaining propositions in this section assume the axiom of choice:
17) Here we are assuming the axiom of a life mission beyond material indulgence].
18) Assuming the axiom of choice and, given an infinite cardinal κ and a finite cardinal μ greater than 0, the cardinal ν satisfying __FORMULA__ will be κ.
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