With one of my grade 7 classes, we were discussing powers of 10, and we had built a whole scale, from ten up to one million, using decimal and exponential notation. When we reached the point where they had to express 1 in exponential notation, most of the students were perplexed. I guided them through the process of inferring from the sequence of previous exponents what the next exponent should logically be and managed to elicit 100. It gave them food for thought because they have probably been warned time and time again against the uncanny properties of zero and most of them had rather not fret with that moody animal too much. Some did venture out and stripped this surprising 0 up there, changing the base, scratching their little heads until the substance emerged. Whatever base they tried, raising it to the power 0 gave 1! And A. went timidly, in his characteristic manner: ’Teacher, what about infinity? Does infinity raised to the power 0 equal 1 as well?’
This was one of the best questions I’ve had over the past few months. This kid, A., is passionate about big numbers and the concept of infinity just blows his mind. I caught him writing the symbol for infinity all over his notebooks. Some can’t live without mangas, others feel for infinity…each to their own!