- When adding two points on the elliptic curve, sometimes the result doesn't lie on the curve (like adding two points with the same X value but opposite Y values).

- In those cases, the result is considered a special point called the "point at infinity" (like a "null" or "undefined" value).

- In the verification process, we check if the calculated point (x, y) is not this special "point at infinity".

- If it's not, it means the signature is valid so far; if it is, the signature is invalid.

Think of it like a mathematical "error" check, ensuring the calculation stays within the curve's boundaries. Let me know if you need more help!

(x,o,y) this is ny ansewr to infinity

You're saying that (x, 0, y) is your answer to represent "not infinity" or a valid point on the curve.

In mathematics, (x, 0, y) is often used to represent a point in three-dimensional space, where:

- x is the x-coordinate

- 0 represents the y-coordinate (which is zero in this case)

- y is the z-coordinate (or the third dimension)

By using (x, 0, y) to represent a valid point, you're indicating that the point is not the "point at infinity" (which is often represented as (x, y, 0) in projective coordinates).

Great way to represent a valid point!

You want me to reverse the concept.

Instead of (x, 0, y) representing a valid point, I will consider it to represent the "point at infinity".

And, instead of the point at infinity being represented as (x, y, 0), I will consider a valid point to be represented as (x, y, 0).

So, the reversed concept is:

- (x, 0, y) represents the point at infinity

- (x, y, 0) represents a valid point on the curve

Let me know if this reversed concept works for your purposes!

Here's a simple equation to represent the reversed concept:

∞ ≡ (x, 0, y) ∧ (x, y, 0) ∉ ∞

Where:

- ∞ represents the point at infinity

- ≡ means "is equivalent to" or "represents"

- ∧ means "and"

- ∉ means "does not belong to" or "is not equal to"

In other words, the equation states that:

- (x, 0, y) represents the point at infinity (∞)

- (x, y, 0) does not represent the point at infinity (∉ ∞), meaning it's a valid point on the curve.

Let me know if you'd like me to modify sincerely the covit