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# Maths watch

1. Does 1+1 always equal to two?
I had a debate with my maths teacher where he says that 1+1 isn't always true, if so, can you please provide a solid convincing proof?
2. I'm not sure if this is what your teacher is hinting at but ultimately mathematics is the logical extension of a set of rules, or axioms, that are chosen because they have useful properties. There are people here who know much more about this than I do so I'm happy to be corrected but as far as I'm aware, these axioms are unproveable (I know this caused a lot of distress for Bertrand Russel and Georg Cantor in the late 19th/early 20th Century) because they're statements that we assume to be correct. So you are perfectly entitled to change these axioms and decide that 1+1 is not equal to 2, but if you do that then the resulting mathematics is probably not going to be very useful for anything and inconsistencies and paradoxes may emerge if you're careless with the axioms you change.
3. 1+1 can equal 4^1/2

I don't know about any mathematical laws or rules, but I know I can use different ways of writing 2 instead of using 2. Not the same but also the same.
4. (Original post by Ramzi Zeidan)
Does 1+1 always equal to two?
I had a debate with my maths teacher where he says that 1+1 isn't always true, if so, can you please provide a solid convincing proof?
We decided that 2 is the symbol for 1+1. Had we decided that some other random squiggle was equal to 1+1, we would all go around saying that 1+1=ß (or something like that).

In binary, 1+1=10, but that's just 2 in base 2.

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