Which of the following statements is NOT true for sets of numbers?
1. Well, the first is true: any whole number can be written as a fraction, for example
2 = 2/1 = 4/2 = 6/3, etc. And a fraction, when it’s a whole number divided by another, that’s exactly what a rational number is.
The second is also true, and for the same reason, including negative numbers. This is what happens when we want subtraction to always work: we have to invent or figure out these negative integers and put them in too.
Third: yes, that is also true. Real numbers include rational numbers and irrational numbers (and irrationals include transcendental numbers! Like pi and “e”, which are “non-algebraic”, meaning you can’t calculate them using the usual operators: addition, subtraction, multiplication, division, exponents, or roots of integers… oops, but they weren’t asking for all that, were they?
Fourth: bingo, it’s the one you want, it’s the fake one. All rational numbers are not integers, one exception suffices to prove it, and 1/2 is a rational number which is not an integer, so there – or, QED – or, that’s it!
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