#### Please [explain like I’m 5 years old](https://www.howtogeek.com/694298/what-does-eli5-mean-and-how-do-you-use-it), compare and contrast ALL 4 symbols =, ≡, ↔, ⇔.
All answers beneath are too knotty and byzantine to my secondary school daughter.
– https://math.stackexchange.com/q/500644
– https://math.stackexchange.com/q/3926367
– https://math.stackexchange.com/q/2432462
## https://math.stackexchange.com/q/4645583
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These are all symbols that assert a *relation* between two objects. Relationships can include things like equality (`=`), greater than (`>`), taller than, heavier than, has more calories than, etc.
`=` most frequently is used to indicate *equality.* What equality means depends on the context, but for in the context of numbers, and the sake of simplicity you can take it to mean “numerically equal” (the same number). That’s not really what it means, but in order to define the formal definition of equality we’d have to start talking about a particular axiom system, and that’s not ELI5.
`≡` often means equivalence or congruence, which has different meanings in different contexts. In geometry, you might say two different triangles are congruent to each other—what that means has its own definition. In modular arithmetic, you might say two expressions are equivalent “modulo some integer.” Again, the definition of equivalence varies depending on how you’re using it.
`↔` Often means “if and only if,” also known as a biconditional. It is used in logical propositions. I.e., it is part of the vocabulary in the language of making claims or statements that are either true or false. An example is “Bob will eat the ice cream if and only if it is vanilla flavored.”
In order to understand biconditionals, it’s helpful first to understand the conditional `→`, which indicates an “if…then” relationship. For example, “If Sparky is a dog, then Sparking has four legs.”
`⇔` Is very similar, but has to do with logical implication. Implication means one statement follows from another. A two way implication would mean a statement follows from another, and vice versa. The difference is `→` relates two expressions, and `⇒` relates two statements.
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