3 ms·
It's not sloppy notation. It's an unambiguous infinite series of the form sum_n=1^infinity 9/10^n that converges to 1. It's the same reason that 0.333... = 1/3
by jjmarr 2y ago
It's not sloppy notation. It's an unambiguous infinite series of the form sum_n=1^infinity 9/10^n that converges to 1.
It's the same reason that 0.333... = 1/3. It's an infinite series that converges on 1/3.
Students learn repeating decimals before they understand infinite series.
- astrobe_ 2y agoIt is ambiguous, that's the trick. One can interpret "..." as '"any number of 9s", and in this interpretation the equation is false. But the teacher will eventually ask, "what about an infinite number of 9s"? Bam! brilliant introduction to series and convergence. The correct notations to express exactly what one means feature the infinity symbol [1] - but if you use them, well, of course the students will see the trap. [1] https://en.wikipedia.org/wiki/Infinity#Real_analysis https://en.wikipedia.org/wiki/Infinity#Real_analysis