Abstract
In the last several chapters we discussed proof techniques for universal statements of the form
in this chapter we focus on the existential quantifier and analyze existential statements of the form
For instance, we may claim that a certain equation has a real number solution (the existence of \(\sqrt{2}\), to be formally proven only in Chap. 23, is a prime example), or we may claim that a certain set has a minimum element (by Theorem 13.6, every nonempty set of natural numbers does). Quite often, we deal with statements of the form
for example, when in Chap. 1 we claimed that a certain game had a winning strategy for Player 2, we made an existential statement that for any sequence of moves by Player 1, there was a response by Player 2 that resulted in a win for Player 2.
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© 2013 Béla Bajnok
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Bajnok, B. (2013). Existential Proofs. In: An Invitation to Abstract Mathematics. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6636-9_15
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DOI: https://doi.org/10.1007/978-1-4614-6636-9_15
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