/sci/ - Science & Math

>>12001752
>(-inf, inf) isnt well defined until after you define it
No, this interval is a well-defined object. Saying the unbounded, open 1D interval is not defined until I define it is like saying the Latin alphabet's characters aren't defined until I define them.

>This symbol is defined to be this other undefined thing
Furthermore, even in that case where I concede your wrong proposition that (-inf, inf) is not as pre-defined as the letters I'm writing with, I use infinity to define R, and I don't use R to define infinity. In pic related definition of infinity at the bottom of page 4, this definition does not require R. This definition satisfies the Cauchy definition of a limit with [math] x\in\mathbb{Q} [/math]. Your stupid criticism of the form, "This pseudo-circular definition collapses upon inspection," is wrong and it is as retarded as you are.