There is a question in a book is: if
1+101=110 is a proposition or not.
The author said it's not a proposition, since it's true if the numbers are binaries, is false if the numbers are decimals. So we can't figure out if it's true or false, that it's not a proposition.
But in the book of "Discrete Mathematics and Its Applications", it says
1+1=2 is proposition:
1+101=110 is not a proposition, that
1+101=102 should not be a proposition, that
1+1=2 should not be a proposition.
I'm confused about this question and answer, how to understand it correctly?
I tried to translate the original text to English, sorry for my poor English.
I will give you some examples to explain the concept of proposition.
- Chinese people are great
- Snow is black
- There are living things on the other stars
- All of you, stand at attention！
- Shall we have a meeting tomorrow?
- What a nice day!
- I'm lying.
- I'll learn English, or Japanese.
- If it's sunny, I will go for a walk.
For the examples above, (1)(2)(4)(9)(10) are propositions. For (4), although we don't know if it's true or false for now, but we will know it someday, so we can say it's a proposition. (3) is true if they are binaries, false if they are decimals, so it's truth value is depended on the context.