Statements and Quantifiers

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Ace

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the statement " for some real numbers x, x2≥0 is true. However your friend does not understand why, because he claims that x2≥0 is true for all real numbers x and not some. How would you explain his misconception to him?

I dont understand the problem at all
 
Ace said:
the statement " for some real numbers x, x2≥0 is true. However your friend does not understand why, because he claims that x2≥0 is true for all real numbers x and not some. How would you explain his misconception to him?
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All you have to do is the ask him:
  1. Is minus two a real number?
  2. Is the square of minus two a positive number?
  3. Is it then true that some real number squared is positive?

There you have it.
 
Ace said:
the statement " for some real numbers x, x2≥0 is true. However your friend does not understand why, because he claims that x2≥0 is true for all real numbers x and not some. How would you explain his misconception to him?

I dont understand the problem at all
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Or, to put it a different way, if it is true for all of the real numbers then it is certainly true for some of the real numbers.
 
Ishuda said:
Or, to put it a different way, if it is true for all of the real numbers then it is certainly true for some of the real numbers.
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You don't really think that, do you?

All unicorns are blue. So some unicorn is blue.
 
pka said:
You don't really think that, do you?

All unicorns are blue. So some unicorn is blue.
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Well, I think so but every once in a while I have to stop and re-think so let's see. Suppose we assume the opposite: It is not true that some unicorn is blue. If it is not true that some unicorn is blue I think that means that all unicorns are not blue because if there were a unicorn which was blue then that unicorn could be the 'some unicorn' which is blue. So we would have all unicorns are not blue. But we are given that all unicorns are blue. So that only leaves one of two conclusions
(1) Some unicorn is blue or
(2) Unicorns don't exist (in which case all unicorns are also pink). But please don't tell me unicorns don't exist, that would destroy some of my grandchildren and great grandchildren and great great grandchildren's faith in the universe, not to mention put a large dent in mine.
 
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