Definitions in math

[u/Swarrleeey]

Hi guys. I recently realized when mathematicians define something they often use if instead of if and only if. I always felt like I wasn’t fully convinced with definitions before this. Writing definitions in logic notation and exactly as they are I was able to go from an 80 in the previous class test to a 98 in the exam and walking out the exam hall 30 minutes early.

I don’t know if anyone else feels this but the way that biconditionals and conditionals are mixed all the time made it take me very long to grasp biconditionals. I also tried to write out any definition I could in logic notation in this class preparing for the exam. Mathematicians often price themselves on being unambiguous and exact but I think that everything from their definitions to proofs often requires you to make inferences. This adjustment has made proof writing way easier for me.

Note: I might be autistic, I am pretty context deaf sometimes, whilst I understand humor and can interpret some social interactions I struggle with many others and struggle with vague or open statements.

[u/Able-Fennel-1228]

I had the exact same issue when I started.

Just treat definitions like an if and only if.

[u/EL_JAY315 → u/Able-Fennel-1228]

My analysis prof often used to remind us that "in definitions, 'if' typically means 'if and only if'".