We should also observe that it is important to know precisely where in the sentence a given connecting word is introduced. For example, compare the following two sentences: 1. For every positive number x there exists a positive number y such that y<x. 2. There exists a positive number y such that for every positive number z, we have y<x. Although these statements may look similar, they do not say the same thing. As a matter of fact, (1) is true and (2) is false.

bergvolk0k

bergvolk0k

Answered question

2022-10-29

We should also observe that it is important to know precisely where in the sentence a given connecting word is introduced. For example, compare the following two sentences:
1. For every positive number x there exists a positive number y such that y2. There exists a positive number y such that for every positive number z, we have yAlthough these statements may look similar, they do not say the same thing. As a matter of fact, (1) is true and (2) is false.

Answer & Explanation

Bridget Acevedo

Bridget Acevedo

Beginner2022-10-30Added 19 answers

The first sentence says, for every positive number x you name, name a smaller positive number y. Sure, take y = x 2 ,
The second sentence says there's a positive number y that's smaller than any positive number x you can name. How does that work?

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