# 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.

axiom collocations

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 sentences

5) 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 axiom

15) 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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