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Is there any branch of mathematics in which it is false that If A = B, then B = A ? ?
Can the logical inference
If A = B, then B = A
ever be false? Is there an algebra or type of logic or math entity in which this can be false?
4 Antworten
- PuzzlingLv 7vor 5 MonatenBeste Antwort
The relation "is equal to" is the canonical example of a binary equivalence relation which is reflexive, symmetric and transitive.
If the equal sign (=) is being used to represent the "is equal to" relation, then it is always true that:
A = A (reflexive)
A = B → B = A (symmetric)
A = B, B = C → A = C (transitive)
But it is possible to redefine the meaning of the equal sign to where this wouldn't be true. So how are you defining '='?
- Anonymvor 5 Monaten
Statement A = all dogs are 4 legged creatures.
Statement B = All 4 legged creatures are dogs.
B is not equal to A but A = B.
Logic could be such branch.
But if A and B are numbers, then it can't be false.