Real number arithmetic

Algebra Level 2

Let $a$ and $b$ be 2 real numbers. Which of the following are not necessarily real?

A) $a+b$

B) $a-b$

C) $a \times b$

D) $a \div b$

A They are all real D B C

1 solution

Ayush G Rai
Nov 8, 2016

Let us take a to be some real number and b to be $0.$ So when we plug in the values for all , we get $A,B,C$ to be real but not $D$ because $\dfrac{a}{0}$ cannot be determined and hence is not a real number. Therefore the answer is $\boxed{D}.$

Poor question!

Andreas Wendler - 4 years, 7 months ago

hahaha.yes

Ayush G Rai - 4 years, 7 months ago

Poor as in easy, or poor as in what?

Sharky Kesa - 4 years, 7 months ago

I did it similarly, as well!

Rico Lee - 4 years, 7 months ago

Can undefined even be considered a "number", and thus be assigned as either a "real" or "nonreal"? The question could have been easily interpreted as: Assuming the values of A, B, C, D are well defined, are they real? It's somewhat awkward to say that a value that cannot be defined is definitely nonreal, unless a concrete definition poses otherwise.

Bryan Hung - 4 years, 7 months ago

Then why isn't imaginary numbers considered under real numbers.

Ayush G Rai - 4 years, 7 months ago

I'm discussing undefined numbers, not complex.

Bryan Hung - 4 years, 7 months ago

@Bryan Hung – ok well if they undefined numbers are not real then should be under "non-real".

Ayush G Rai - 4 years, 7 months ago

@Ayush G Rai – How does one even classify an undefinable number as either real or nonreal? It's literally not a defined value, so how can the question be valid?

Bryan Hung - 4 years, 7 months ago

@Bryan Hung – A number that isn't real can be undefined. An undefined expression is just that, not real. Bryan, this question is indeed valid, but you're over-thinking what undefined expressions are.

Sharky Kesa - 4 years, 7 months ago

same way +1

A Former Brilliant Member - 4 years, 5 months ago

thanks neel !!

Ayush G Rai - 4 years, 5 months ago

Real number arithmetic

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