Playing With Infinity

[nycmathguy]

1. What e^(infinity)?

2. What is pi^(infinity)?

Can this be calculated without a calculator?

 

[Country Boy]

It's not a good idea to play with infinity- you could get hurt!

Neither e^infinity nor pi^infinity has any meaning. "Infinity" is not a real number so none of the operations on real numbers is defined for infinity. There are several different ways to extend the real numbers to include infinity (some of them with a single "infinity", some with "positive infinity" and "negative infinity", some with many "infinities") but they still do not include these operations.

 

[nycmathguy]

It's not a good idea to play with infinity- you could get hurt!

Neither e^infinity nor pi^infinity has any meaning. "Infinity" is not a real number so none of the operations on real numbers is defined for infinity. There are several different ways to extend the real numbers to include infinity (some of them with a single "infinity", some with "positive infinity" and "negative infinity", some with many "infinities") but they still do not include these operations.

Get hurt? God is eternal. He has been good to me.