Reply to Re: I gave up to the Computers National Olympiad
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And really, why wouldn't there be a square root of a negative number? Why would (a little less than) half of our "known" real numbers be left out of the joy of having a square root? That's just rubbish!
It's not rubbish. If you say "what is the square root of X?" you are in fact also saying "what number multiplied by itself equals X?" So if X is a negative number you a question that has no logical answer. Here is why:
- Say X is 4.
- The square roots of 4 are 2 and -2.
- However is X is -4 the same does not hold. Here is why:
* Positive times positive = positive * Whenever you multiply a even number of negatives you get a positive number.
In other words -X has no even root. It does however have a odd root.
In short, no real numbers exist that give us -X when they have a even power. Meaning -X squared does not have a logical answer if you use real numbers. Hence complex numbers also being called "imaginary numbers".
as for being consistent, i think the above information makes it clear that constiency is laking when you try to use real numbers.
It's not rubbish. If you say "what is the square root of X?" you are in fact also saying "what number multiplied by itself equals X?" So if X is a negative number you a question that has no logical answer. Here is why:
- Say X is 4.
- The square roots of 4 are 2 and -2.
- However is X is -4 the same does not hold. Here is why:
* Positive times positive = positive * Whenever you multiply a even number of negatives you get a positive number.
In other words -X has no even root. It does however have a odd root.
In short, no real numbers exist that give us -X when they have a even power. Meaning -X squared does not have a logical answer if you use real numbers. Hence complex numbers also being called "imaginary numbers".
as for being consistent, i think the above information makes it clear that constiency is laking when you try to use real numbers.
