Albion College Mathematics and Computer Science Department

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.

Upcoming Events

Recent News

3/5 - Math/CS Colloquium: Stavros Christofi
3/14 - Pi Day
4/2 - Math/CS Colloquium: Eric Mann, `74

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For further information contact:
David Seely, Acting Chair
Department of Mathematics and Computer Science
Albion College
Albion, Michigan 49224-5013
mathcs@albion.edu
(517) 629-0361

Food for Thought

To solve the equation x^{x^{x^{·^{·^·}}}}= 2, notice that the exponent of the base x is the same as the entire left-hand side of the equation. Hence the equation can be rewritten x² = 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^{x^{x^{·^{·^·}}}}= 4 similarly leads to x⁴ = 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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Albion College ◦ Albion, Michigan ◦ 517/629-1000