

Welcome!
The Mathematics and Computer Science Department at
Albion College includes the disciplines of pure and applied
mathematics, computer science, and statistics. The department
offers majors and minors in Mathematics and
Computer Science. See our links on the left for more details.
For further information contact:
David Seely, Acting Chair
Department of Mathematics and Computer Science
Albion College
Albion,
Michigan 492245013
mathcs@albion.edu
(517) 6290361 



Food for Thought
To solve the equation x^{xx
···}= 2,
notice that the exponent of the base x
is the same as the entire lefthand side of the equation.
Hence the equation can be rewritten x^{2} = 2.
It follows that x =
is a solution to the equation.
In other words, when is substituted
for x in the tower of exponents,
the value of the expression is 2.
Now the equation x^{xx
···}= 4
similarly leads to x^{4} = 4.
So x = =
is a solution to this equation.
In other words, when is substituted
for x in the tower of exponents,
the value of the expression is 4.
It appears that for x =
the tower of exponents has the value of both 2 and 4.
Does this mean that 2 = 4?
Answer
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