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How to Think Like a Mathematician by Kevin Houston

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CHAPTER 11

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Complexity and negation of quantifiers

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Everything is simpler than you think and at the same time more complex than you imagine.

Johann Wolfgang von Goethe

The more quantifiers a statement has the more complicated it is and the harder it is to understand. In this chapter we will look at how complicated statements can be made with quantifiers and give a method for seeing through this complexity.

We also see how to negate statements involving quantifiers. Fortunately, even for the most complicated of statements this is actually quite easy. ...

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