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1284179
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location San Mateo, CA
age 59
visits member for 4 years, 1 month
seen 2 hours ago

2h
comment Square root and principal square root confusion
That's right. In some cases it is useful to put the $\pm$ sign in front of the square root
2h
answered Square root and principal square root confusion
14h
awarded  irrational-numbers
1d
answered Create a Ray from two points
1d
answered Is it true that $\lim_{ x\to a}(f(x)/g(x)) = f(a)/g(a)$ without the assumption $g(a)\ne 0$?
1d
comment Inner product and unit vector
That is correct.
1d
comment How can I prove that no derivative exist withing this function?
@Masacroso: I think we are at a much lower level with this question. It looks to me first year calculus. Even so, what value would you assign for $f'(0)?$ I think distributions do not care about the value at a point.
1d
comment Does the definition of derivative exclude the possibility for discontinuous rate of change?
You seem to think that $10^{-7}$ is automatically small. It is not. Functions and their derivatives can do anything in that interval. It is not hard to find a nice smooth function that meets your specs (aside from $1=7$ and the like). We just need to make sure the $h$ in the definition of derivative is smaller than $10^{-7}$, but that is OK.
1d
comment Inner product and unit vector
You are given the vectors in the problem statement. Now take any vector $(a,b)$, express it as a linear sum of $u_1,u_2$ and use linearity.
1d
answered There exists a positive real number $u$ such that $u^3 = 3$
1d
answered Inner product and unit vector
1d
answered How can I prove that no derivative exist withing this function?
1d
comment Prove that there is an integer $N$ such that $\frac{N}{10^k} \leq x \lt \frac{N+1}{10^k}$
You need to look at the definition of the floor function. You are trying to justify that every real is between two integers (inclusive on the low side).
1d
answered Prove that there is an integer $N$ such that $\frac{N}{10^k} \leq x \lt \frac{N+1}{10^k}$
1d
comment Prove that there is an integer $N$ such that $\frac{N}{10^k} \leq x \lt \frac{N+1}{10^k}$
You need to be clear that $k$ is an number that is given to you, not one you are allowed to choose. It is also true if you get to choose $k$, but I suspect that going forward you will need to use the fact that $k$ is given to you.
1d
comment How to show that the product of two irrational numbers may be irrational?
@BarryCipra: Thanks. It doesn't need transcendence, so I learned something, but it is still a big fact.
1d
answered Probability of two points being part of two segments of different size
1d
reviewed Approve suggested edit on How to show that the product of two irrational numbers may be irrational?
1d
comment Probability of 8 or 9 digit sequence colliding in the same place in two 65 digit numbers
In response to your edit: note there are $10$ digits in the $36$ through $45$ places. I presume you mean the $8$ digits to be $36$ through $43$. In that case, the $10^{-8}$ of the two answers applies.
1d
answered How to show that the product of two irrational numbers may be irrational?