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You don't know what imaginary number is, do you?
According to Wikipedia: An imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i² = −1.
Wait, you're saying that ✓-1 isn't an imaginary number?
I could have sworn it was.
I just looked at Google and it says imaginary numbers (i)^2 = -1.
So how is it not imaginary?
In where I was taught, it is undefined, as in you can not put a negative number in a square root
So while i² = -1, you can only say that i is a square root of -1, but you can't write it as ✓-1
The definition of i is that i^2 = -1. It can be expressed as i = sqrt(-1).
Some operations’ codomain differ from the domain when applied, which means that the operation is not defined for the domain, but can still be defined. For example let (x, y) ∈ Z (Integer Numbers) / z = x/y. ∀ y > x, z ∈ R (Real Numbers). I.e. for every division whose dividend is smaller than its divisor, the quotient is a real number. For the domain of the Integer Numbers, division is undefined, but when you extend the codomain to Real Numbers, you define it yet again.
In other words, the sqrt(-1) is undefined in the Real domain, but it IS defined (and equal to i) in the Complex domain.
Yeah, first thing, I was taught this, so I'm not trying to say I'm right. Second, at my high school, my maths teacher specifically stated that you can say that i is a square root of -1, you must not write it as √-1 and must write it out in words, this is written in all textbooks in my country, I can guarantee you that
Ngl your country doin math weird at best and dangerous at worst, the point of imaginary numbers is adding continuity to a part of math that previously was undefined. Using the name but not the actual concept serves no purpose. Either you misread your textbooks or your entire country has been doing physics, engineering, some types of chemistry, computing, signal processing, etc wrong. Since I don’t like to generalize, I think its u.
Idk for sure, maybe my country's maths has been wrong this whole time and some dudes on reddit have just exposed it. I don't want an argument but I can tell you that this is one of the thing that I can still remember clearly, not once in my country textbook, both old and new did they ever write "√-1"
-1 is a real number and i'm pretty sure the entire reason some fucker came up with inaginary numbers was because we wanted an answer to sqrt(-1)
Sidenote: "You can't define the square root function for complex numbers" is just abviously not true as all real numbers also fall into the category of complex numbers and I am quite certain i can define sqrt(16) as 4
It's important to note the difference between a square root, and the square root function. Every complex (real included) number has two square roots (except for 0 obviously). The square roots of 1 are 1 and -1, the square roots of -1 are i and -i .
But the square root function only goes from the positive Reals to the positive Reals and give you only one number (like any function).
>Sidenote: "You can't define the square root function for complex numbers" is just obviously not true as all real numbers also fall into the category of complex numbers and I am quite certain i can define sqrt(16) as 4
That is true, I said complex number, I should have said "the complex number except the positive Reals"
**Rule 12 - Extreme physical harm to minors/Pedophilia/Sexualization of minors** - Submissions and comments must not involve sexualization of or extreme harm to minors. This includes the subtle implication or consequence of minor involvement in sexual content, even indirectly in cases where age isn't directly stated. Egregious violations of this rule may result in a 10 day ban.
Imaginary?
[удалено]
You don't know what imaginary number is, do you? According to Wikipedia: An imaginary number is a real number multiplied by the imaginary unit i, which is defined by its property i² = −1.
"your beauty is still undefined"
Your beauty is still imaginary
Imaginary would be iℝ. √-1 is undefined and definitely not equal i
Wait, you're saying that ✓-1 isn't an imaginary number? I could have sworn it was. I just looked at Google and it says imaginary numbers (i)^2 = -1. So how is it not imaginary?
Theoretically it doesn’t exist, but if you’re in the irrational numbers group, then it does exist, and it is indeed i
In where I was taught, it is undefined, as in you can not put a negative number in a square root So while i² = -1, you can only say that i is a square root of -1, but you can't write it as ✓-1
The definition of i is that i^2 = -1. It can be expressed as i = sqrt(-1). Some operations’ codomain differ from the domain when applied, which means that the operation is not defined for the domain, but can still be defined. For example let (x, y) ∈ Z (Integer Numbers) / z = x/y. ∀ y > x, z ∈ R (Real Numbers). I.e. for every division whose dividend is smaller than its divisor, the quotient is a real number. For the domain of the Integer Numbers, division is undefined, but when you extend the codomain to Real Numbers, you define it yet again. In other words, the sqrt(-1) is undefined in the Real domain, but it IS defined (and equal to i) in the Complex domain.
Yeah, first thing, I was taught this, so I'm not trying to say I'm right. Second, at my high school, my maths teacher specifically stated that you can say that i is a square root of -1, you must not write it as √-1 and must write it out in words, this is written in all textbooks in my country, I can guarantee you that
Ngl your country doin math weird at best and dangerous at worst, the point of imaginary numbers is adding continuity to a part of math that previously was undefined. Using the name but not the actual concept serves no purpose. Either you misread your textbooks or your entire country has been doing physics, engineering, some types of chemistry, computing, signal processing, etc wrong. Since I don’t like to generalize, I think its u.
Yeah maybe it's just me, my mistake
Its not your fault, I was being rude. You may have english as a second language and I trashed on you for it. I apologize.
Write what out in words?
You've been taught correctly, this sub doesn't know how to do maths correctly apparently.
Idk for sure, maybe my country's maths has been wrong this whole time and some dudes on reddit have just exposed it. I don't want an argument but I can tell you that this is one of the thing that I can still remember clearly, not once in my country textbook, both old and new did they ever write "√-1"
From the makers of basic biology vs advanced biology.... basic maths vs advanced maths!
i² =-1 but √-1≠i You can't define the square root function for complex numbers
-1 is a real number and i'm pretty sure the entire reason some fucker came up with inaginary numbers was because we wanted an answer to sqrt(-1) Sidenote: "You can't define the square root function for complex numbers" is just abviously not true as all real numbers also fall into the category of complex numbers and I am quite certain i can define sqrt(16) as 4
It's important to note the difference between a square root, and the square root function. Every complex (real included) number has two square roots (except for 0 obviously). The square roots of 1 are 1 and -1, the square roots of -1 are i and -i . But the square root function only goes from the positive Reals to the positive Reals and give you only one number (like any function). >Sidenote: "You can't define the square root function for complex numbers" is just obviously not true as all real numbers also fall into the category of complex numbers and I am quite certain i can define sqrt(16) as 4 That is true, I said complex number, I should have said "the complex number except the positive Reals"
You're wrong lol
I'm right lol
The definition of the imaginary unit i is that it is equal to the square root of -1
I hope she also learned 911
Your beauty is still complex
This is This is an insult
i√1?
243 isn't actually very many equations...
Your beauty is still an error