One of founding pillars of mathematics is that you cannot divide by zero; ...
Therefore, if one starts claiming that division by zero isn't absurd because it pops up while solving some problems.
I think then it would cast a lot of doubt on the credibility of mathematics and give rise to disbelief in mathematics.
Another one of the founding principles of mathematics is that when you multiply any two 'real' numbers you will get a +ve number;no matter even if the numbers were -ve.
Now when we write sqrt(-1), we are trying to do something which isn't allowed.
Hi
One of founding pillars of mathematics is that you cannot divide by zero; it's utterly absurd. Therefore, if one starts claiming that division by zero isn't absurd because it pops up while solving some problems. I think then it would cast a lot of doubt on the credibility of mathematics and give rise to disbelief in mathematics.
Another one of the founding principles of mathematics is that when you multiply any two 'real' numbers you will get a +ve number;no matter even if the numbers were -ve. Now when we write sqrt(-1), we are trying to do something which isn't allowed. I think I don't have much problem with writing swrt(-1) and calling it iota. Obviously, I would have serious problem accepting the result if it was said that sqrt(-1) equals some real number. So, I think my problem only lies in the fact that how come we end up with sqrt(-1) expression while solving other 'normal' problems. How does nature make use of such 'nonsense' expression? Could you please give me some simple example where iota is used and we can make some sense out of it? I don't think nature can make much use iota when one can't even tell which one the two or more imaginary numbers is greater; e.g. you can't tell whether 4i is greater than 2i or not! Please don't use more math to explain math. Thank you.
Regards
PG
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misterT,
Like many other descriptions of "j" or "i", I would fault it because it does not emphasize that j or i is a mathematical operator. They seem to treat it as a esoteric constant that does not have a well defined value in the real world, which is untrue. See my post #3 in this thread.
Ratch
i is not an operator, it is an imaginary number (constant) which has a real part of 0 and imaginary part of 1. Re(i)=0, Im(i)=1. Emphasizing i as an operator is a very big fault.
How would you explain multiplying two operators, i*i = -1? Doesn't make sense.. unless i is not an operator, but a number.. a constant.
But what does simple 7j mean? Rotate by 90°? Please keep your exposition simple.
I think what obstructs people like me from accepting j or i as an operator is the fact that it is not entirely like other operators such as + or x. You can saybut you can't speak of, let's say, addition operator as "+ = (something)".
Now, prove to me that you understand the concept. Find the value of j^j without using arithmetic or a calculator. Just use Euler's Identity and rotations to find the value.
Find the value of j^j without using arithmetic or a calculator. Just use Euler's Identity and rotations to find the value.
I understand the concept of thinkin i as an operator, but it still is only a constant (imaginary unit).
I can easily calculate with imaginary numbers without using i (or j).
Here is an example of i*i. Because Re(i) = 0, and Im(i)=0, I get:
Re(i*i) = 0*0 - 1*1 = -1
Im(i*i) = 0*1 + 1*0 = 0
I don't need the symbol i.. I only need to know the imaginary part and real part to do complex calculation. The constant i only makes using complex numbers easier.
I can also write: i = e^(i*θ)
where θ defines the complex argument, or "the amount of rotation", not i "as an operator of rotation".
How does the operator concept fit into this form?
How is it wrong to think the constant j as a constant (imaginary unit)?
Can you prove it is not a constant?
Well, j^j = e^(-π/2)
But I don't see what this has to do with the "operator" concept. I would like to see you solve that only with Euler and rotations.
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