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The context telling whether equality, equivalence, or congruence is to be understood.
When I read the last sentence, I thought its meaning is "we need to understand the context telling whether equality, equivalence, or congruence ". Is that right?
Could someone explain to me what "to be understood" actually means in this sentence? Thanks for any help.
The context tells us whether the 'sign of equality' is to be understood as meaning equality, equivalence or congruence - that is, what meaning is intended in a particular case.
The "sign of equality" is the equals sign: i.e., "=".
It's a complicated sentence, and you're parsing it incorrectly; "to be understood" does not modify "context" but "equality, equivalence, or congruence".
The book is saying that there is no single symbol that everybody uses for "is congruent to". Some teachers use symbols like ≅ or ≡ for this, but more often they use the symbol = for all of equality, equivalence, and congruence, and you need to use context to understand which of them it means.
