Explore Math & Theories Behind 2=-2

In summary, the equation 2=-2 is an identity that is always true and challenges our traditional understanding of equality. It can be used in complex number systems and has applications in fields like electrical engineering. The concept of 2=-2 is supported by mathematical theories such as complex numbers and abstract algebra, highlighting the power and flexibility of mathematics.
  • #1
fahraynk
186
6
Does this relationship come out anywhere interesting in math? Are there any anything interesting theories built with this at its foundations?
$$2=2*1=2*\sqrt{1}=2*\sqrt{(-1*-1)}=2*i*i=2*i^2=-2$$
 
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  • #3
First of all square root does not come out of nowhere.

If y^2 = 1 then y=±(1)^(1/2). That means y is +1 or - 1.

Next i is a special complex unit in the form of (0,1) where as 1 is a real number. A REAL NUMBER CANNOT BE REPRESENTED AS PURELY COMPLEX.

<Edited>

A real number system is a subset of Complex number system but the converse isn't true.I assume that this was a random post from a popular social media. The most of them are baseless, only written to attain popularity. Don't waste time on them.
 
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  • #4
e-pie said:
-3=sqrt(3) x i^2 FALSE
##-\sqrt{3}## is indeed equal to ##\sqrt{3} \times i^2##

Edit: I'd failed to notice that the claimed inequivalence could rest in part on the obvious fact that 3 <> ##\sqrt{3}##. I've repaired that oversight and hope that I've now rendered the intended claim properly.

What is not true is that ##\sqrt{-1} \times \sqrt{-1}## is equal to ##\sqrt{-1 \times -1}##.
 
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  • #5
square roots are two valued functions. The roots are always of opposite sign. In deriving an expression, make sure you have the right sign. Otherwise you get silly things like ##4=4##, ##\sqrt{4}=\sqrt{4}##, therefore ##2=-2##.
 
  • #6
mathman said:
square roots are two valued functions.

Yikes! How many threads are there where sudents are lectured that ##y = \sqrt{x}## is a function ? (i.e. not a "multi-valued" function).

"Square root" is an example of ambiguous terminology in mathematics. "##y## is equal to the square root of ##x##" has one definition as a function. If ##x^2 = y## then ##x## is a square root of ##y## has a different definition, which describes a property of ##x##.

In complex analysis no one blinks at speaking of "the n-th roots of unity". or even "multi-valued" functions.
 
  • #7
Stephen Tashi said:
Yikes! How many threads are there where sudents are lectured that ##y = \sqrt{x}## is a function ? (i.e. not a "multi-valued" function).

"Square root" is an example of ambiguous terminology in mathematics. "##y## is equal to the square root of ##x##" has one definition as a function. If ##x^2 = y## then ##x## is a square root of ##y## has a different definition, which describes a property of ##x##.

In complex analysis no one blinks at speaking of "the n-th roots of unity". or even "multi-valued" functions.
You can argue about terminology, but the fact remains 4 has two square roots, 2 and -2. This is the source of many silly proofs, such as in the original post!
 
  • #8
mathman said:
You can argue about terminology, but the fact remains 4 has two square roots, 2 and -2.
Yes, no one disputes that, but by common agreement, the symbol ##\sqrt 4## evaluates to a single number, + 2.

The OP's question has been answered, and there are multiple threads here about this "paradox" and similar ones, so I'm closing this thread.
 

Related to Explore Math & Theories Behind 2=-2

1. What does 2=-2 mean in math?

The equation 2=-2 is a statement that says two is equal to negative two. This is known as an identity, which means that it is always true no matter what values are substituted for the variables.

2. How is it possible for 2 to equal -2?

In traditional mathematics, it is not possible for a positive number to equal a negative number. However, in certain mathematical systems such as complex numbers, the concept of equality can be extended to include values that are not typically considered equal in real numbers.

3. Can you provide an example of when 2=-2 would be used in real life?

One example of when 2=-2 could be used is in electrical engineering, specifically in alternating current (AC) circuits. In these circuits, the current and voltage oscillate between positive and negative values, and the equation 2=-2 can represent the peak values of these oscillations.

4. What theories or concepts support the idea of 2=-2?

The concept of 2=-2 is supported by mathematical theories such as complex numbers and abstract algebra. These theories extend the concept of equality to include values that are not traditionally considered equal in real numbers.

5. Why is understanding 2=-2 important in math?

Understanding 2=-2 is important because it challenges our traditional understanding of equality and shows that there are other mathematical systems where this concept can be extended. It also demonstrates the power and flexibility of mathematics to handle complex and abstract concepts.

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