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May
24
comment What does a probability of $1$ mean?
@vadim123 so where are you in the chat?
May
24
comment What does a probability of $1$ mean?
@ruakh oh sorry, I see now.
May
24
comment What does a probability of $1$ mean?
@vadim123 The probability of picking number with such beginning is not zero. But where is the number, whose picking probability is zero?
May
24
comment What does a probability of $1$ mean?
@vadim123 so give an example of a number that you picked randomly from 0 to 1.
May
24
comment What does a probability of $1$ mean?
@vadim123 give an example of such picked number.
May
24
comment What does a probability of $1$ mean?
area zero=probability zero. Not 1. Proportional, not backward proportional. -1
May
24
comment What does a probability of $1$ mean?
Your example does not prove anything: probability of choosing an integer is zero, AND you never will choose an integer. So probability zero means never happens. Completely wrong answer -1
Jan
9
comment If $f(x)+f'(x)-\frac{1}{x+1}\int_{0}^{x}f(t)dt=0$ and $f(0)=0$, then what is $f'(x)$?
@nbubis I have re-checked and came to the same result.
Jan
9
comment If $f(x)+f'(x)-\frac{1}{x+1}\int_{0}^{x}f(t)dt=0$ and $f(0)=0$, then what is $f'(x)$?
@nbubis I also corrected the conclusion: actually there ARE non-trivial solutions, yet the condition does not specify a unique one.
Jan
9
comment If $f(x)+f'(x)-\frac{1}{x+1}\int_{0}^{x}f(t)dt=0$ and $f(0)=0$, then what is $f'(x)$?
@sun I fixed the typo, thanks. The result does not change, it was only a typo when I copied it here.
Jan
9
comment If $f(x)+f'(x)-\frac{1}{x+1}\int_{0}^{x}f(t)dt=0$ and $f(0)=0$, then what is $f'(x)$?
@nbubis I fixed the typo, thanks. The result does not change, it was only a typo when I copied it here.
Dec
20
comment How to calculate $f(x)$ in $f(f(x)) = e^x$?
Seems this post does not answer the question. The questioner did not look for an entire function and even for funtions on the complex plane at all.
Nov
10
comment The interpretation of $0 \cdot \infty$
You can manipulate $\infty$ in the extended real line. But still for that number multiplication by zero is indefinite.
Nov
6
comment Can exponentiation and power function be defined through Albert Bennett's operations?
@Lubin there is no supposed distributivity, # is zero-order operation, before addition, and * is a 3rd order operation, after multiplication, it is distributive against multiplication.
Nov
6
comment Can exponentiation and power function be defined through Albert Bennett's operations?
@sos440 I just used my own notation. If I had access to his paper I would change it.
Nov
5
comment Is $0^0=1$ postulate independent of all other axioms of complex numbers?
@JavaMan in that case his answer seems incomplete.
Nov
5
comment Is $0^0=1$ postulate independent of all other axioms of complex numbers?
@JavaMan thanks, the author claims that this leads to certain exceptions in limits laws so I asked for some examples in the comment.
Nov
4
comment Zero to the zero power - Is $0^0=1$?
0^0 is undefined by whom? I saw somebody defined it, can I now say it is defined?
Nov
4
comment Zero to the zero power - Is $0^0=1$?
"otherwise it would lead to all sorts of exceptions when dealing with the limit laws" - can you please give some examples of such exceptions?
Nov
4
comment What is the value of $\lim_{x\to 0} x^i$?
So the limit of the absolute value is 1 and the limit of the argument in infinity, right?