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There's a strange number system, featured in the work of a dozen Fields Medalists, that helps solve problems that are intractable with real numbers.

If you don't mind, i have a small query.As the Topic of the thread is 0...I was Wondering..Are there any fields of knowledge in which 0 is attributed a (+) or (-) sign?Have you ever come across a +0 or -0 value?Thanks!

What we usually call algebraic numbers are finite additions of one or more root numbers which have 0 imaginary component, or 0 argument in polar coordinate.

Math Has a Fatal Flaw//www.youtube.com/watch?v=HeQX2HjkcNoQuoteNot everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer.The video title sounds bombastic, perhaps deliberately to increase views.IMO, the paradox and confusion comes from how we treat infinity.Quotehttps://brilliant.org/wiki/infinity/Infinity is the concept of an object that is larger than any number. When used in the context "...infinitely small," it can also describe an object that is smaller than any number. It is important to take special note that infinity is not a number; rather, it exists only as an abstract concept. Attempting to treat infinity as a number, without special care, can lead to a number of paradoxes.Infinity is not a number!QuoteBecause infinity is not a number, it requires special rules of arithmetic in order to remain consistent. This is a useful view in fields such as measure theory, which extends the real numbers by adding two numbers ∞ and −∞, that satisfy some additional rules:a+∞ = ∞+a = ∞ (for any a besides −∞)a−∞ = −∞+a = −∞ (for any a besides ∞)a⋅∞ = ∞⋅a = −∞ (for positive a)a⋅∞ = ∞⋅a = −∞ (for negative a)a/∞ = a/-∞ = 0 (for real a)∞/a = ∞ (for positive a)∞/a = -∞ (for negative a)It is worth noting that 1/0 is not ∞. Additionally, operations involving multiple infinities (such as ∞−∞ and ∞/∞) are not generally well-defined.Importantly, note that this is an extension of the real numbers chosen specifically to allow infinity to be treated as a number; without this context, infinity remains a concept rather than a number. For instance, the following sections continue to treat infinity as a concept rather than a number, because the measure theory context above no longer applies

Not everything that is true can be proven. This discovery transformed infinity, changed the course of a world war and led to the modern computer.

https://brilliant.org/wiki/infinity/Infinity is the concept of an object that is larger than any number. When used in the context "...infinitely small," it can also describe an object that is smaller than any number. It is important to take special note that infinity is not a number; rather, it exists only as an abstract concept. Attempting to treat infinity as a number, without special care, can lead to a number of paradoxes.Infinity is not a number!

Because infinity is not a number, it requires special rules of arithmetic in order to remain consistent. This is a useful view in fields such as measure theory, which extends the real numbers by adding two numbers ∞ and −∞, that satisfy some additional rules:a+∞ = ∞+a = ∞ (for any a besides −∞)a−∞ = −∞+a = −∞ (for any a besides ∞)a⋅∞ = ∞⋅a = −∞ (for positive a)a⋅∞ = ∞⋅a = −∞ (for negative a)a/∞ = a/-∞ = 0 (for real a)∞/a = ∞ (for positive a)∞/a = -∞ (for negative a)It is worth noting that 1/0 is not ∞. Additionally, operations involving multiple infinities (such as ∞−∞ and ∞/∞) are not generally well-defined.Importantly, note that this is an extension of the real numbers chosen specifically to allow infinity to be treated as a number; without this context, infinity remains a concept rather than a number. For instance, the following sections continue to treat infinity as a concept rather than a number, because the measure theory context above no longer applies

Any number can be represented with a finite amount of information or digital bits of information. It's just that you can't have this ability for all numbers simultaneously.

Have you found an answer to the question "how many numbers exist"?