User blog comment:Sbiis Saibian/Introduction to Googology/@comment-168.212.150.41-20151110203629

This is overall a good page, but there is one very ignorant statement regarding infinity, in which the author asserts that any stament that uses infinity in the definition will return infinity, which is simply false. Now, obviously I could think of an easy counter-example to show what I mean such as 1/infinity, but then people would just say "well, obviously any expression with infinity is either infinite or zero, still not interesting" which is ALSO false. For example, consider an interesting expression:

(2^0.5)^^Infinity This looks like it OBVIOUSLY equals infinity, right? WRONG. Believe it or not, the above expression is equal to 2; as you evaluate the power tower for more and more steps, the value converges to 2. And this is just one example. I think you're wrong to instantly write off infinity, it may have some interesting properties, potentially including ones we don't know about yet. Oh and if you don't believe me about the above expression equalling 2, do some research or try it yourself, but if you try it, MAKE SURE YU EVALUATE THE POWER TOWER RIGHT-TO-LEFT. if you go left to right, it WILL converge to infinity.