@shredalert Stay active but don't exert yourself. Namely, when tired during exercise, stop and rest. Don't push yourself unnecessarily, because not everyone have the same physiological limits. =)
Also, ECCs are fun! Even more so if you construct them yourself! I had lots of fun designing my own ECCs, though of course it's nowhere near the state of the art called LDPC codes, which is actually near the Shannon limit but I don't know much about them. For instance Hamming codes can correct any 1-bit error. What if you want to correct any 2-bit error? =)
@user21820 I only recently got some free time to study. I'm currently doing the section on converting natural language to basic sentential. In terms of graph theory, I only just started the book. Haven't had the time to get around to it.
I've also been reading an applied topology book and been watching Gilbert Strang's linear algebra lectures before bed.
@shredalert I see. Have you seen this quote "you cannot fool all the people all the time."? Note the ambiguity and find 3 possible interpretations and their precise first-order forms. After that look at the original quote here and determine the intended interpretation! =)
@Zophikel: You can go ahead and ask. But why not as a question on Math SE?
Well I'm having trouble with your grammar and spelling. I think you can do better..
But as I said, you could just post your question on Math SE, together with your attempted proof, if you want to ask for proof verification and feedback.
You don't use things on other things, just like it makes no sense to ask whether you can use differentiation on triangles... However, if you want to ask whether | integrate { f(x) : x in [a,b] } | <= integrate { | f(x) | : x in [a,b] } is true, then yes it is true, but do you know why?
Under the condition that integrate { f(x) : x in [a,b] } exists in the first place, of course.
Let $f$ be a continuous and integrable function over $[a;b]$. Prove or disprove that
$$\int_a^b |f(x)|\ \mathrm{d}x\geq \left | \int_a^b f(x)\ \mathrm{d}x\right|
$$
@user21820 it's an induction based proof with lots of inequality, absolute values and integrals :(, so i'm having a little trouble justifying correctly what the author did
@SimplyBeautifulArt I didn't even know two of my friends were getting married until I got an invitation. I kind of forgot about it as well because I was reading a book in my favourite series that day......
Oops, I meant to say I'm running out of steam! Pure inspiration and/or feeling respected helps me generate more steam! You all help me restore my inspiration; and of course I feel respected just as I respect you all. I've just taken a hard hit, which has nothing to do with you all!
@SimplyBeautifulArt reminds of of a children's book about a little red engine trying to make it up a mountain: "I think I can....chug, chug...I think I can...chug, chug...etc"
@shredalert Yes indeed; always good advice for any one of us to remember the little things that make us smile.
Hehe, while p > 0, please repeat and set p = p + 1: "I think I can... chug, chug..." p = 1 "I think I can... chug, chug..." p = 2 "I think I can... chug, chug..." p = 3 "I think I can... chug, chug..." p = 4 ......................................................
$$\text{if you're happy and you know it } \to \text{ clap your hands }...$$ $$\text{if you're happy and you know it } \to \text{ clap your hands }...$$
First two lines from a song we sang when I was 8 years old! ....and are followed by "if you're happy and you know it, then your face will really show it...clap your hands."
The fast growing hierarchy (FGH) is a personal favorite of mine because I think it is not only simple compared to things involving trees or the BB function, while still being able to outgrow, say, the Ackermann function.
First, a simple layman's explanation of what FAIL approximately does:
Th...
@amWhy XD
I updated my answer to produce a much more natural/layman explanation on fast growing functions that I hope most people would understand
:| You know, I'm honestly wondering what my life is gonna be like
1. Will I accomplish something worthwhile in mathematics? 2. Will I be happy with my relationships? 2.1. Will I be happy with my girlfriend/wife? 3. Will there be a decent Earth? 4. Will there be enough sweets for me? 5. Will I raise a good family? 6. Will I be happy with my job? 7. Should I preserve myself as a robot?
$(P)$ $$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \frac{dy}{dt} = f(t,y), y(t_o)=c_o $$
Remark: Our IVP, defined in $(P)$ carries the following assumptions: values of $f(t,y)$ are within the set of real numbers, and are continuous.
$$Lemma \, \, (0)$$
$\,\,\,\,\,\,\,\,\,...
Let $f$ be a continuous and integrable function over $[a;b]$. Prove or disprove that
$$\int_a^b |f(x)|\ \mathrm{d}x\geq \left | \int_a^b f(x)\ \mathrm{d}x\right|
$$
The fast growing hierarchy (FGH) is a personal favorite of mine because I think it is not only simple compared to things involving trees or the BB function, while still being able to outgrow, say, the Ackermann function.
First, a simple layman's explanation of what FAIL approximately does:
Th...
$(P)$ $$\, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \, \frac{dy}{dt} = f(t,y), y(t_o)=c_o $$
Remark: Our IVP, defined in $(P)$ carries the following assumptions: values of $f(t,y)$ are within the set of real numbers, and are continuous.
$$Lemma \, \, (0)$$
$\,\,\,\,\,\,\,\,\,...
This is the Realm of Simply Beautiful…
This is the Realm of Simply Beautiful…