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How to Think Like a Mathematician by Kevin Houston

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CHAPTER 10

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Quantifiers – For all and There exists

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You can fool all the people some of the time, and some of the people all the time, but you cannot fool all the people all the time.

Abraham Lincoln

In Chapter 6, Making a statement, we called a sentence like ‘x is an odd number’ a conditional statement. Whether or not it was true depended on x. In this chapter we shall describe two fundamental ways of quantifying x so that we get statements rather than conditional statements.

We can exemplify them via the following. The sentence ‘x2 = 2’ is conditional ...

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