Equivalence-I.mp3
Equivalence-I.mp4
Equivalence-Unplugged-Underground-XVI.mp3
Equivalence-Unplugged-Underground-XVI.mp4
Equivalence-intro.mp3
[Intro]
(I meant)
Reflexivity
(Symmetry)
Transitivity
(Equivalent)
[Verse 1]
If by the chance
The equivalence
Has relevance
To our circumstance
[Bridge]
(I meant)
Reflexivity
(Symmetry)
Transitivity
(Equivalent)
[Chorus]
When true is true
(The same truth value)
The influence
(Of congruence)
[Verse 2]
Love and romance
Is there equivalence
Is there a debate
With evil and hate
[Bridge]
(I meant)
Reflexivity
(Symmetry)
Transitivity
(Equivalent)
[Chorus]
When true is true
(The same truth value)
The influence
(Of congruence)
[Outro]
(I meant)
Reflexivity
(Symmetry)
Transitivity
(Equivalent)
A SCIENCE NOTE
Meaning of Equivalence in Math and Science
1. In Mathematics:
- Equivalence refers to a relationship between two objects that are considered equal in some specific way, even if they are not strictly identical.
- It is often defined through an equivalence relation, which must satisfy reflexivity, symmetry, and transitivity (e.g., congruence of geometric figures, modular arithmetic, etc.).
- In logic, equivalence (⇔) means two statements have the same truth value.
2. In Science:
- Physics: Equivalence often refers to fundamental principles like the Equivalence Principle in General Relativity, which states that gravitational and inertial mass are equal.
- Chemistry: Equivalence can describe equivalent weight, meaning the amount of a substance that reacts with or replaces a standard amount of another.
Symbol for Equivalence
- ≡ (Triple bar) → Used in logic and mathematics to denote strict equivalence (e.g., identity relations, logical equivalence).
- ∼ or ≈ → Used to indicate approximate equivalence.
- ≅ → Used for geometric congruence or structural similarity.
- ⇔ → Used in logic to indicate “if and only if” (logical equivalence).