I am a square, the youngest I can be, but not a baby.
but not the multiplied by one.
I'm not a mishearing of no.
My friends call me strange.
But, I am not only one.
What am I?
Complete explanation of main riddle for acceptance.
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I guess that you are:
-1
I am a square, the youngest I can be, but not a baby.
-1 = i ^ 2, where i is the unit imaginary number.
The 'not a baby' rules out zero, based on the4kman's answer and user_194421's subsequent update to the question.
but not the multiplied by one.
This rules out 1 (or +1) as being the square
I'm not a mishearing of no.
This rules out 0 ("oh") and 4.
When my friends asked me, "What is your area?", I said I have none.
Positive squares can be considered as the representation of an area, whereas -1 cannot.
They called me strange as a result.
This does not fit in with conventional (physical) examples of numbers, hence is strange (and the associated numbers are therefore called complex numbers).
But, I am not only one.
Because you are minus one.
What am I?
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2
Are you
0?
I am a square, the youngest I can be
Zero is the smallest non-negative number, and the square of 0.
but not the multiplied by one
Zero is not the square of 1.
I'm not a mishearing of no
You are not "four".
When my friends asked me, "What is your area?", I said I have none
A square with sides of 0 has an area of 0.
They called me strange as a result
If you get 0 as a result, it's unusual (you might've been miscalculated something, e.g. multiplied something with 0).
But, I am not only one
You are not one (since you are 0).
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2$\begingroup$ How is "four" a "mishearing of no"? The fact that your answer isn't 4 is irrelevant. What about "Oh"? $\endgroup$ – John Coleman Jan 19 '18 at 16:04
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