# What does this infinitive mean? 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.

• You’ve given us what you thought it means but you haven’t told us what the sentence is. Mar 8, 2021 at 10:25
• sorry i have editted it again
– J_KI
Mar 8, 2021 at 10:32
• You’re asking about the infinitive (that is, “to be understood”). What difficulty do you have with it? Mar 8, 2021 at 10:54
• Actually, I‘m not familiar with usage of infinitive in different cases.Like "to be understood"in this sentence.So I don't know what author want to say exactly.
– J_KI
Mar 8, 2021 at 11:36
• ' ... or congruence is to be understood by the reader' // ' ... or congruence is meant in the example in question'. Mar 8, 2021 at 11:43

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.

• thank you very much
– J_KI
Mar 8, 2021 at 13:31

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.

• Thank you for taking your time in explaining the question.
– J_KI
Mar 8, 2021 at 13:25
• I suppose that for full understanding, it should be made clear that some methods need an equivalence indicator rather than an equality indicator. In ax + 7 ≡ 3x + b, a = 3 and b = 7. The initial statement is true for all values of x, as with say 3(x + 2) ≡ 3x + 6. Mar 8, 2021 at 15:20