"The true metaphysics of the square root negative 1 remains elusive." - C.F. Gauss

[IBDaMann]

Infinity isn't a quantity. It has no size.

How many integers are there?

 

[Into the Night]

so stop playig word games.

Playig??

Attempted random phrase. No apparent coherency.

 

[Into the Night]

How many integers are there?

NaN.

 

[Bai Lan]

NaN.

does this mean Not a Negro?

 

[Bai Lan]

How many integers are there?

hmmmmm.

that's a toughy.

a gazillion?

 

[Bai Lan]

Reporter: what do you think of the recent changes in the Brazilian Dollar?

George W Bush: Boy that's a lot of money!

 

[Cypress]

Good choices. The world needs mechanics and ditch diggers too. From what I can tell, only about a third of the population of any country, at most, is college material. Another third or so are people who can do skilled trades that are every bit as important to a modern society as skills derived from college. Then there's the last third. The world needs hairdressers and janitors too...

I don't begrudge anyone who took auto shop in high school, rather than college prepatory math classes.

I just don't think they should howl in protest if people who did take college prep math in 11th and 12th grade want to discuss an article on the theory, application, and philosophy of numbers.

 

[Cypress]

Nope. You and Trumpet are flat out denying math just because you both believe everything you read on the internet. All you had to do was to look up the mathematical proof that i does not equal -1, but as you demonstrated, learning is simply too much work for you.

You were talking about visualization and conceptualization.

Until high school students get to the level of advanced algebra or precalculus, teachers only instruct them in the use of real numbers. That's why you believe the square root of negative one is impossible.

It's not impossible. It's only impossible for the positive numbers on real number line.

The terms 'real' and 'imaginary' numbers are historical relics which come from a time when mathematicians were still debating the meaning of complex numbers. These days, complex numbers are universally accepted and have real world applications. As the engineers on this thread stated.

 

[IBDaMann]

NaN.

It is a number to those who have conceptualized it as such.

 

[IBDaMann]

hmmmmm. that's a toughy. a gazillion?

There are infinite integers. There are also infinite natural numbers. The quantity of natural numbers and the quantity of integers is equal.

In fact, the individual quantities of natural numbers, whole numbers, integers and rational numbers are all equal, called denumerably infinite.

The quantity of irrational numbers and of real numbers, however, while also being infinite, is of a larger infinity than the denumerably infinite, and it is called nondenumerably infinite.

Now that you have learned this, you probably want to adopt an endangered baby harp seal.

 

[Bai Lan]

There are infinite integers. There are also infinite natural numbers. The quantity of natural numbers and the quantity of integers is equal.

In fact, the individual quantities of natural numbers, whole numbers, integers and rational numbers are all equal, called denumerably infinite.

The quantity of irrational numbers and of real numbers, however, while also being infinite, is of a larger infinity than the denumerably infinite, and it is called nondenumerably infinite.

Now that you have learned this, you probably want to adopt an endangered baby harp seal.

that seems like too many.

 

[IBDaMann]

Until high school students get to the level of advanced algebra or precalculus, teachers only instruct them in the use of real numbers. That's why you believe the square root of negative one is impossible.

Incorrect. According to mathematics, the square root of negative numbers cannot be taken. Of course, you never learned this because you never finished middle school where this is taught to all children. Stay in school in your next life, no matter how difficult learning is for you.

All you had to do was to research the mathematical proof showing that it is invalid to take the square root of negative numbers, but as you continue to demonstrate, learning is too difficult for you. You would rather deny mathematical proofs.

It's not impossible.

It's not allowed.

It's only impossible for the positive numbers on real number line.

You are denying math because you are too lazy to learn and because you will believe anything you read on the internet.

These days, complex numbers are universally accepted and have real world applications. As the engineers on this thread stated.

Yes. Irrelevant. It is not permissible to take the square root of a negative number.

 

[IBDaMann]

that seems like too many.

It seems that way, but it falls just shy of "too many."

 

[Bai Lan]

It seems that way, but it falls just shy of "too many."

yes. infinity is less than too many.

I knew it.

 

[Cypress]

It's not allowed.

Many polynomial equations do not have solutions on the real number number line.

You have two choices.

Throw up your hands in surrender and declare that most polynomial equations are unsolvable and simply have no solutions.

Or you can open your mind to the mind to the possibility that your concept of abstract numbers was too limited, and there exists a whole other abstract concept of number on the complex plane.

 

[Into the Night]

does this mean Not a Negro?

Not a number.

 

[Into the Night]

hmmmmm.

that's a toughy.

a gazillion?

It's Nan. Not a number.

 

[Into the Night]

I don't begrudge anyone who took auto shop in high school,

Yes you do. Don't try to deny your own posts!

rather than college prepatory math classes.

Do you know trigonometry? You'll need it to build a house (or even a shed!). Do you know how to calculate the volume of a cylinder? You'll need it for automotive work.

WTF is a 'college prepatory math class'?????

I just don't think they should howl in protest if people who did take college prep math in 11th and 12th grade want to discuss an article on the theory, application, and philosophy of numbers.

Numbers are not a philosophy. Numbers are not a theory. Numbers are not an application. Numbers are just that...numbers.

You're bullshitting again.

 

[Into the Night]

Until high school students get to the level of advanced algebra or precalculus, teachers only instruct them in the use of real numbers. That's why you believe the square root of negative one is impossible.

Algebra does not use the square root of -1. Neither does calculus. It is not possible to take the square root of -1.

It's not impossible. It's only impossible for the positive numbers on real number line.

Reversal fallacy. You can take the square root of any positive value.

The terms 'real' and 'imaginary' numbers are historical relics which come from a time when mathematicians were still debating the meaning of complex numbers.

They are not historical relics. Math is not a relic.

These days, complex numbers are universally accepted and have real world applications. As the engineers on this thread stated.

And it is still not possible to take the square root of a negative number.

 

[Into the Night]

Many polynomial equations do not have solutions on the real number number line.

The number line is not a 'solution'.

You have two choices.

Throw up your hands in surrender and declare that most polynomial equations are unsolvable and simply have no solutions.

No complex number needed.

Or you can open your mind to the mind to the possibility that your concept of abstract numbers was too limited, and there exists a whole other abstract concept of number on the complex plane.

Abstract is not a number. Complex numbers are not a plane.

You are bullshitting again.