==hoomank (hooman@mit.edu) == 
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 Hello. I noticed the comment on infinity being the state of "being greater than any other number." I think there are some issues with this defintition so I wonder if you've considered the two following arguments. 

 1. The section is titled "mathematical infinity" yet the definition does not apply to all mathematical systems including Calculus! 

 The definition given "the state of being greater than any other number" is not applicable to Calculus where infinity means "to grow without bound"  a definition which makes sense in the context of a limit  to see why, see point 2 below. 

 2. The given definition seems to run into philisophical problems. 

 The definition given is that "infinity is the STATE of being greater any other number" 

 The word "state" usually refers to something static. When we say, for example, that something is in a solid state  we mean that the atoms at that moment, have come together to form a solid.  

 There is no such state as "being greater than any other number."  For no matter what number you are at, there are ALWAYS numbers greater than you. Thus this state does not exist. 

 One defensible defintion of infinity is the calculus definition which is to "grow without bound." For instance in Calculus we say that the limit as X approaches 0 of 1/X = infinity. By this we mean that the value grows without bound as X gets closer to 1  but we never say that it is in the state of being greater than any number  which is the current definition. 

 I am going to change the mathematical infinity section to "there are a number of logically defensible definitions of infinity." Feel free to change this sentence but please do not change it back as the current definition does not seem to be defensible.