If the sum of all real numbers equals zero, then isn't zero the center of the math universe?

Answer 1

I think you could say that, even for imaginary numbers, and I think you'd convey some valuable information of what zero means.

However, dealing with infinity, something that's really not a number, is a little problematic. You can set things up to prove just about anything.

For example: Which has more points: a circle or a line?

Each has an infinite number of points, but that doesn't mean they have an equal number of points. In fact, for every point on the line, I could draw a new line that intersects two points on the circle without ever crossing over any points twice - that proves there must be twice as many points in a circle as in a line, right?

The second problem is that zero really identifies your origin, which is relevative to what you're trying to measure, rather than absolute. In other words, if you're at home wanting to know how far you have to travel to work, the fact that your home is 75 miles from Denver, not zero, really isn't relative to what you're trying to find out. As far as you're concerned, wherever you're at is zero.

You also find some unbalanced functions, which seriously dilutes the symmetry you're trying to convey. For example, try graphing the values of (-2)^x power. What you'll find is why that's an illegal function*. That function won't even work if you expand your domain to complex numbers. Exponential functions like a^x are only defined when a>0 and not equal to 1.

So saying zero is the center of the math universe would fall apart as soon as you started looking a little closer.

Edit: * That probably needs a little clarification on why that function doesn't work. -2 squared is 4. -2 cubed is -8. Where exactly does that function cross zero?

Answer 2

Uh, can you prove that negative infinity exists? And, are you trying to construct a series that asymptotes to zero, then calling that the center?

Furthermore, for completeness, is zero the center of the imaginary numbers? The zero at the center of your math universe looks like a black hole.

Answer 3

Using your logic, you would first have to assume that real numbers are the centre of the math universe, and then you could say that 0 is the absolute centre of the math universe.

In reality, the real numbers are only a part of mathematics. They are a large part of mathematics, and have a place in all fields (pun intended), but there is so much out there, they are not more important than all the other stuff.

Answer 4

While your predicate is true, your conclusion can't be reached because you haven't defined your terms. What do you mean "the center of the math universe"? That's a terribly vague concept. Without clarification how can anyone agree or disagree?

Answer 5

But the sum is not absolutely convergent!

By changing the order of summation, any number can be attained as the sum of all real numbers.

Answer 6

Yes, that is correct. The number halfway between infinity and minus infinity is zero.

Answer 7

Yeah

Answer 8

Yes, isn't it cool that way? Zero is where it is at!

Answer 9

0 is a concept, just a tool, use it for what ever you can, 0 is relative only to what your doing.

Answer 10

of course it is.