1- Give an example of natural numbers whose difference is not a natural number; give an...
1- Give an example of natural numbers whose difference is not a natural number; give an example of natural numbers whose quotient is not a natural number.
As you can see, subtractions and divisions are operations that cannot be performed within the set of natural numbers.
Consider the number system Q containing all fractions (positive and negative); subtractions and divisions are now always possible (with the exception of dividing by 0); however, the operation "take the limit of a sequence of numbers" cannot always be performed in Q.
2-Think of a sequence of numbers where each number in the sequence is a quotient of two \textbf{natural} numbers, but the limit is not [hint: think of the golden ratio];
Now let's consider the operation of taking power.
3- How much is 2 to the power of 1/2 ? Do you think this number is in Q? In R? How can you be sure that it is not in Q?
4- How much is -1 to the power of 1/2? Is this in Q? in R?
Have a good weekend!
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1- Give an example of natural numbers whose difference is not a
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