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16 Μαΐ 2021 · Formal proof: I followed it for a while until to the $0\le 1-x\ldots$ line, then I got lost in how it was trying to prove. Algebraic arguments: I don't follow how this one works, because, say $x = 0.99$ (To simplify things, it could be $0.999$ if wanted), $10x = 9.9$ $10x = 9+0.9$ while in the argument it stated
- Is 0.9 repeating = 1 disproved by asymptotes?
I'm discussing proofs that 0.9 repeating equals 1 with some...
- Formal proof for $(-1) \\times (-1) = 1$ - Mathematics Stack Exchange
By the distributive law, $(x + 1)(x - 1) = x^2 - 1$. Set $x...
- Is 0.9 repeating = 1 disproved by asymptotes?
I'm discussing proofs that 0.9 repeating equals 1 with some friends, and they use asymptotes to disprove this. One says if we had the function $y=x/0.000\ldots1$ (and he's only using that impossible
13 Ιουν 2020 · By the distributive law, $(x + 1)(x - 1) = x^2 - 1$. Set $x = -1$ and observe that the left hand side is zero, so the right hand side is zero, so $x^2 = 1$. It's arguable whether the assumptions I use there are any more or less obvious than the conclusion.
How to prove that a number to the zero power is one. Why is (-3) 0 = 1? How is that proved? Just like in the lesson about negative and zero exponents, you can look at the following sequence and ask what logically would come next: (-3) 4 = 81. (-3) 3 = -27. (-3) 2 = 9. (-3) 1 = -3. (-3) 0 = ????
17 Απρ 2022 · For example, if the backward question is, “How can we prove that two real numbers are equal?”, one possible answer is to prove that their difference equals 0. Another possible answer is to prove that the first is less than or equal to the second and that the second is less than or equal to the first
The following is a “proof” that one equals zero. Consider two non-zero numbers x and y such that. x = y. Then x 2 = xy. Subtract the same thing from both sides: x 2 – y 2 = xy – y 2 . Dividing by (x-y), obtain. x + y = y. Since x = y, we see that.
The Proof. The statement that we want to prove is: 0.99999999… = 1. Note that the 3 dots after the 9s mean ‘recurring’, i.e. that there are an infinite number of nines after the decimal point. Let x=0.9… Then 10x = 9.9… So 10x – x = 9x; but also 10x – x = 9.9… – 0.9… = 9 (Many people get lost here.
