A brief history of infinity : the quest to think the unthinkable

"We human beings have trouble with infinity--yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity--yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an a...