Question

. A rational number can be represented in the form of (where p,q are integers and q ≠ 0)


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Answer 1

Answer:

yes it's true

Step-by-step explanation:

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Answer 2

$\huge\pink{Answer}$

Kind of! According to the logical definition of a rational number, as provided by Dedekind, it is because if one “cuts” the real number line at n=0, there will be a maximum of the set of ratios before the cut (ie: 0/n). If there were only a limit but no maximum, the number would be irrational. For example, the set of ratios approaching pi would have no maximum because no ratio is equal to pi. However, it will have a limit equal to pi.

Also, by the definition you provided above, it would also be a rational number because 0 is an integer and 0/m is m is some integer will always be numerically equal to the integer 0.

The reason I say “kind of” at the beginning is because by the definition of a rational numbers, just 0 would not be a member because 0 is the class of classes similar to the empty class and a ratio is a relation(xRy). For example, p/q is defined as a relation given two classes of similar classes, p and q such that xp=yq. In order to define the relation, two numbers, p and q, are needed. In that case, 0 would not be a ratio and would therefore, not be a rational number whereas 0/n would be if n is specified as being a class of similar classes in the posterity of 0 would be although they are numerically equal.

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