1≤1 proof

[Nickfytas]

A friend asked me how 1+1≤2 and I couldn’t convince him , and asked me if there is a mathematical proof and the only thing i could think is to assume this as not true and end up with something not true (1>1) .can anyone help me with a better proof

 

[Dr.Peterson]

A proof at this level requires agreement on axioms and definitions. What does your friend accept as given, on which a proof can be based?

 

[pka]

A friend asked me how 1+1≤2 and I couldn’t convince him , and asked me if there is a mathematical proof and the only thing i could think is to assume this as not true and end up with something not true (1>1) .can anyone help me with a better proof

Does you friend play by to rules in all games. That is not meant as a frivolous question.
Every proof is based upon a set of axioms( rules for deductions). Does your friend accept that \(0<1~?\)
Then \(0+1<1+1=2~?\) If one then surely the other. If not the one then by what rules is he/she playing?

 

[topsquark]

A friend asked me how 1+1≤2 and I couldn’t convince him , and asked me if there is a mathematical proof and the only thing i could think is to assume this as not true and end up with something not true (1>1) .can anyone help me with a better proof

Perhaps this is a little more basic than that. Does your friend agree that 1 + 1 = 2? The notation [math]1 + 1 \leq 2[/math] is shorthand for one of the two possibilities
1 + 1 = 2 or 1 + 1 < 2. Since the equality holds we can say that [math]1 + 1 \leq 2[/math].

-Dan

 

[Steven G]

I agree with top-square. If your friend agrees that 1+1=2, then you are done.

Does you friend like chocolate ice cream? Assume yes. Does your friend like strawberry ice cream? Assume no. Then it is true that your friend likes chocolate or strawberry ice cream!