Leonardo
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 Nov 27 comment What, if anything, does it mean to be neither finite nor infinite for real numbers? @GitGud I greatly appreciate everyone that offers their knowledge to others. Nov 27 comment What, if anything, does it mean to be neither finite nor infinite for real numbers? @Did it would be like the same thing except factoring out a negative 1. Nov 27 comment What, if anything, does it mean to be neither finite nor infinite for real numbers? Okay that is much more clear, thanks. Oct 25 comment Problem based on Algebraic identities the $3ab^3$ term should be $3ab^2$ Oct 25 comment Problem based on Algebraic identities Perhaps $x$ is an element of some mystical set we are unaware of, I propose $x$ is a duckgoose. Oct 20 comment Tallest bubble tower induction proof I think I see it, when I draw out what you say I can see the tower from $(Center)_1$ to $(Top)_n$ = $\sqrt{n}$. But then knowing that it is scaled by $r$ seems like a leap of faith, but it also seems right, somehow. I am not sure how you saw that connection, but great work. Oct 20 comment Tallest bubble tower induction proof How do you get $r\sqrt{n}$ from the hypothesis? That is the part that I am really confused about. Oct 20 comment Tallest bubble tower induction proof I know how the induction part works, the question is how do I use the inductive hypothesis to show the $n+1$ case = $1 + \sqrt{n+1}$? It is not obvious to me. Oct 6 comment Can a subset have $0$ elements? The empty set is a subset of all sets. Aug 12 comment How do I know what to substitute to simplify a limit? Very interesting, thank you for elaborating that. Aug 12 comment How do I know what to substitute to simplify a limit? This is strange, I thought I could only do that if $t$ approaches infinity. I could have divided the exponents in the original form without substitution and the answer is indeed $2/3$ but I thought it was the wrong method. Aug 9 comment What is another, perhaps quicker and nicer way of solving this question? I really like the way you approach it, always nice to see things from a more focused perspective. Jul 22 comment How would you interpret this question focusing on problem solving? Yeah that clarifies things greatly, I realized that a more rectangle looking shape would make a non-perpendicular. Jul 8 comment Finding points of intersection between a line and a curve Thanks for confirming, the question is probably not the same as this is from my memory. Apr 10 comment How can I determine the values of a third point to make all 3 collinear in $\mathbb{R}^3$ Thanks, I did add the point and was checking it but with no clue what I was doing, but I can figure out why it works soon thanks to your explanation and example. Thank you! Apr 10 comment How can I determine the values of a third point to make all 3 collinear in $\mathbb{R}^3$ I think this is a good answer, but I am lacking so much basic knowledge that it is hard to understand exactly what I am doing. My instinct tells me based on what you say that $3 + t(-2) = 2$ so $t = 1/2$ and $(1/2, 1, -1)$ satisfies the equation? Apr 7 comment What does it mean to be proportional to something? Hm that is interesting, and it confirms my answer when I use the k, that really helps too. It is truly discomforting that my brain does all that without informing me how it was done.. Many thanks! Apr 6 comment Find all values of $a$ such that $w = ai- \frac{a}{3}j$ is a unit vector Thanks a lot, that problem has been bothering me but no longer! Apr 6 comment Find all values of $a$ such that $w = ai- \frac{a}{3}j$ is a unit vector So that would lead me to $a = +\sqrt{\frac{9}{10}}$ and $a = -\sqrt{\frac{9}{10}}$. Does that sound correct? Mar 12 comment How might one go about proving this poorly worded theorem about divisibility with the number 3? The contrast in the clarity between my claim and your theorem is palpable, well done sir.