anonymous
  • anonymous
Which of the following is a counterexample of, "All rational numbers are integers"? is not an integer. 3 is an integer. -1 is a rational number. π is a rational number.
Mathematics
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SOLVED
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chestercat
  • chestercat
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muscrat123
  • muscrat123
what is the ? asking
muscrat123
  • muscrat123
pi is not a rational # i dont think
muscrat123
  • muscrat123
so i believe d can b eliminated

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More answers

anonymous
  • anonymous
oh i for got to add \[\frac{ 1 }{ 2 }\] in front ofther first option
muscrat123
  • muscrat123
but what is the ? asking
anonymous
  • anonymous
i think its to show its a question not a statement
muscrat123
  • muscrat123
by counterexample, it means on the contrary, correct?
anonymous
  • anonymous
i thinik...
zepdrix
  • zepdrix
Hey Audie :) "ALL rational numbers are integers" To show a counter example: Find a rational number which is NOT an integer. That will contradict the ALL of the original statement.
anonymous
  • anonymous
i uh dont no what a integer is... @zep
anonymous
  • anonymous
or i do and forgot
zepdrix
  • zepdrix
an integer is a positive or negative whole number, or zero.
muscrat123
  • muscrat123
What is an integer? Mathematically, integers are set of whole numbers (including zero), and the negative whole numbers: {0, 1, 2, 3, 4, ...} + {-1, -2, -3, -4, ...} In programming, an integer is limited to 32 bits of information, from -2,147,483,648 to 2,147,483,647.
muscrat123
  • muscrat123
an integer can pretty much be any number
anonymous
  • anonymous
so c then?
zepdrix
  • zepdrix
Notice that the 4th option is clearly false. pi isn't a rational number. we don't care about the set of irrational numbers, the statement has nothing to do with them.
zepdrix
  • zepdrix
-1 is a rational number. I'm saying that -1 is also an integer. Hmm, nope. That supports the statement. It doesn't contradict it.
anonymous
  • anonymous
i dont think it could be a because thats 1/2
zepdrix
  • zepdrix
is 1/2 a rational number? is 1/2 an integer?
anonymous
  • anonymous
its not a integer because it says that but i dont think its rational because you cant rationalize it
zepdrix
  • zepdrix
a rational number is a number which can be written as a ratio of integers. Example: 5/2 is a rational number because it's an integer on top and on bottom. 0.15 is rational because we can write it as \(\large\rm \frac{15}{100}\). Again a ratio of whole numbers.
anonymous
  • anonymous
oh so it would be a then...
zepdrix
  • zepdrix
So you've determined: 1/2 is a rational number 1/2 is not an integer Therefore ALL rational numbers cannot possibly be integers. Yessss good job \c:/
anonymous
  • anonymous
thank you for your help!

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