To those of you who have added someone to Rate My Professors, do you usually fill out the email field, or do you guys leave it blank? I know someone who once really did not want their email on that site.

[removed]

Hi! I’m an incoming freshman majoring in biology. I earned credit for calc 2 through calc BC, but I’m currently registered to retake calc 2 because I don’t feel prepared to move directly into calc 3. Since I don’t believe calc 3 is required for my biology major, would it be better that I retake Calc 2, or would it be better to replace it with another course?

Using SPP "logic," we say that 0.999... is 1 - 1/10^n for n∈ℕ going to infinity. Obviously, 1 is a rational number, and the sequence that this produces is (0.9, 0.99, 0.999,...) where each element is clearly rational. Because 1/10^n is never irrational, 0.999... is permanently rational.

Proof by SPP "logic"

Now SPP, you either need to disprove this or accept that 0.999... is rational. If it's rational, show what fraction of integers with nonzero denominator produces 0.999... If the logic is wrong, you need to re-evaluate your logic on why the fact that 1/10^n is never irrational means that 0.999... is rational is false, but how 1/10^n never being 0 sufficiently shows that 0.999... ≠ 1.

SPP, you agree that 1/3 = 0.333..., which means that 0.333... is rational because 1/3 is a fraction of integers where the denominator is nonzero. You also agree that 0.333... * 3 = 0.999..., but this is a problem.

The left-hand side is the product of two rationals, which is always rational by the closure of rationals under multiplication. However, the right-hand side is irrational based on what you say. This is a contradiction, so resolve this now.

I've seen SPP agree in multiple places that 1/3 = 0.333... and that 1/3 * 3 = 1 by what SPP calls "divide negation." I've also seen SPP agree that 0.333... * 3 = 0.999... but somehow still finds that 0.999... ≠ 1. SPP, I will provide what you'd consider a false proof below, and I want you to say where I made any mistakes.

1 = 1/3 * 3 (1) (This is "divide negation.")

= 0.333... * 3 (2) (You've agreed to this previously.)

= 0.999... (3) (You've also agreed to this.)

∴ 1 = 0.999...

SPP, I want you to identify the line(s) with an error. However, based on what I've seen you say in other places, I don't see where you could say that there is an error. To make what I'm asking clear, TELL ME THE LINE(S) WITH AN ERROR. I'm not looking for some explanation on why you think 0.999...≠1; I'm looking for you to tell me where I went wrong in this particular proof my telling me the line number and why what I did in that line is wrong. You should not be bringing nonsense about 0.999... or 0.333... growing endlessly or how 1/10^n is never 0.