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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:26:24
oh great
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Ann
04/17/2022 03:26:25
you could have given other answers
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64bb8913e7b14d06aa9900fca1da50dc
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Ann
04/17/2022 03:26:27
but ok
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64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:26:31
{t-2, t^2-4}
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64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:26:37
this set is linearly independent, as should be clear.
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help-10
64bb8913e7b14d06aa9900fca1da50dc
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Ann
04/17/2022 03:27:04
can you now explain why every polynomial in H can be expressed as a linear combination of these two?
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64bb8913e7b14d06aa9900fca1da50dc
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ibzi
04/17/2022 03:29:10
since they are linearly independent, so everything else would be a linear combination of the two, and hence in the span of the two
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64bb8913e7b14d06aa9900fca1da50dc
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Ann
04/17/2022 03:29:47
no
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:29:58
'linear independence' and 'spanning' are different notions that should not be conflated.
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:30:46
oh why?
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64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:33:13
wym why
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:33:35
just because a set is linearly independent does not automatically mean it spans the space it's in
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:34:05
okay but when it is linearly independent and has the same no. of vectors as the dimension of the space
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:34:14
then it spans it, right?
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Ann
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Ann
false
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64bb8913e7b14d06aa9900fca1da50dc
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Ann
04/17/2022 03:34:14
{x} is a linearly independent subset of P_5 yet you would not claim every polynomial in P_5 is a linear combination of {x} would you?
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:34:44
yes
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:34:52
but it appears you're expected not to use that
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:35:11
and instead show directly that every polynomial in H is a linear combination of your basis (in our case {t-2, t^2-4})
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:37:09
oh okay okay so like this?
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:38:25
$$ a + bt + ct^2 = d (t-2) + k (t^2 - 4) $$
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:39:02
:badtex:
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64bb8913e7b14d06aa9900fca1da50dc
510,789,298,321,096,700
TeXit
04/17/2022 03:39:29
**ibzi**
https://cdn.discordapp.c…650615140362.png
380989650615140362.png
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:39:42
~~and now bad notation + apparent eagerness to plunge headfirst into equation-bashing~~
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:39:57
i mean ok like. sure i guess
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64bb8913e7b14d06aa9900fca1da50dc
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Ann
04/17/2022 03:40:13
you could show that if a + 2b + 4c = 0 then there exist d and k such that what you wrote is true
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help-10
64bb8913e7b14d06aa9900fca1da50dc
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Ann
04/17/2022 03:40:20
if you want to do it like that, who am i to stop you
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help-10
64bb8913e7b14d06aa9900fca1da50dc
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ibzi
04/17/2022 03:40:57
okay then what's the other way
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:41:00
the one you were asking
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help-10
64bb8913e7b14d06aa9900fca1da50dc
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Ann
04/17/2022 03:42:01
i would say that any polynomial in H can be written as (at+b)(t-2)
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:42:22
and that in turn can be written as [a(t+2) + (b-2a)](t-2) = a(t+2)(t-2) + (b-2a)(t-2)
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Ann
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64bb8913e7b14d06aa9900fca1da50dc
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Ann
04/17/2022 03:42:29
which is a linear combination of your basis
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:43:12
oh okay okay
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:43:26
and also how is it bad notation
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:43:44
i personally don't like it, that's how :kekw:
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:43:53
in this particular case i was not being very objective about it
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:44:06
oh lmao okay
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64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:44:31
altho out of curiosity, what did u not prefer?
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:45:07
the d and k do not strike me as good name choices for two constants that should appear related
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:45:45
oh i just used them because i couldn't figure out how to add subscripts
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:46:00
because it italicised my text instead
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:46:10
underscores work just fine
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64bb8913e7b14d06aa9900fca1da50dc
193,692,307,453,771,780
Syst3ms
04/17/2022 03:46:15
@ibzi For the record, my earlier question about factoring was leading to this. Every polynomial such that P(2)=0 is divisible by X-2, so every polynomial in H is of the form (X-2)Q with Q some polynomial. Since we are restricted to degree 2 or less, Q must be of degree at most 1. Since a basis for such polynomials is {...
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64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:46:23
despite discord treating them as italics, the tex bot does them just fine
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help-10
64bb8913e7b14d06aa9900fca1da50dc
183,668,144,404,037,630
Ann
04/17/2022 03:46:39
$c_0 + c_1t + c_2t^2$
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help-10
64bb8913e7b14d06aa9900fca1da50dc
510,789,298,321,096,700
TeXit
04/17/2022 03:46:41
**Ann**
https://cdn.discordapp.c…144404037632.png
183668144404037632.png
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help-10
64bb8913e7b14d06aa9900fca1da50dc
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Syst3ms
04/17/2022 03:46:42
But it was good to yake your time with it
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:47:17
$c_(0) + c_(1)t + c_(2)t^2$
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0
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help-10
64bb8913e7b14d06aa9900fca1da50dc
193,692,307,453,771,780
Syst3ms
04/17/2022 03:47:17
As my teacher says, "the correct method will be whichever one you wind up using"
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:47:25
oh it works without brackets
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:47:41
oh okay okay
1
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:48:14
alright, thanks a lot!
1
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64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:48:21
and sorry for taking up so much of ur time
1
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help-10
64bb8913e7b14d06aa9900fca1da50dc
380,989,650,615,140,350
ibzi
04/17/2022 03:48:41
.close
1
0
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help-10
970b0c072188488c8d52e658c9488421
290,723,508,563,214,340
Poop
11/13/2021 02:26:02
https://cdn.discordapp.c…6846/unknown.png
unknown.png
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help-10
970b0c072188488c8d52e658c9488421
290,723,508,563,214,340
Poop
11/13/2021 02:26:15
can't figure out how to get to 5 as the answer here
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help-10
970b0c072188488c8d52e658c9488421
290,723,508,563,214,340
Poop
11/13/2021 02:49:47
@Helpers
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Ann
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false
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970b0c072188488c8d52e658c9488421
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Poop
11/13/2021 02:59:32
Yeah I just don't get this
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help-10
970b0c072188488c8d52e658c9488421
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Poop
11/13/2021 02:59:41
I can think of more than 5 specific strings that match those requirements
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970b0c072188488c8d52e658c9488421
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Poop
11/13/2021 03:01:23
1000000111111111 1100000011111111 1110000001111111 1111000000111111 1111100000011111 1111110000001111 1111111000000111 1111111100000011 1111111110000001
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714,483,444,394,229,900
Frosty_
11/13/2021 03:03:45
9 sounds like the right answer i think
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Poop
11/13/2021 03:03:57
god I hate my prof lol
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970b0c072188488c8d52e658c9488421
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Poop
11/13/2021 03:04:08
thanks for validating
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Ann
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Poop
11/13/2021 03:04:10
.close
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720b617d6d7b48c2af76d73947bb18d3
943,069,425,274,339,300
PuddinAru
04/17/2022 04:08:23
How?
https://cdn.discordapp.c…096/IMG_0733.jpg
IMG_0733.jpg
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PuddinAru
04/17/2022 04:09:00
How it forces it to be one-one?
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Ann
04/17/2022 04:09:35
isn't that exactly what is explained in the next lines
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Syst3ms
04/17/2022 04:09:55
The fact that it is injective is explained right after
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help-10
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Syst3ms
04/17/2022 04:10:26
Surjectivity isn't too hard to see, because for instance f(f(n)+f(0))=n so every natural number is reached
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PuddinAru
04/17/2022 04:11:03
Yo lol my math’s weak i dont get it
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PuddinAru
04/17/2022 04:11:39
How do you see it?
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Ann
04/17/2022 04:20:27
have you read the lines immediately after the "In fact, we see that"?
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PuddinAru
04/17/2022 04:20:41
Yes
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PuddinAru
04/17/2022 04:20:47
I got it
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PuddinAru
04/17/2022 04:20:50
Thanks
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720b617d6d7b48c2af76d73947bb18d3
193,692,307,453,771,780
Syst3ms
04/17/2022 04:21:58
The definition of surjectivity is that for any number n, you can find an input k such that f(k)=n
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Syst3ms
04/17/2022 04:22:04
i.e every output is reached
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720b617d6d7b48c2af76d73947bb18d3
193,692,307,453,771,780
Syst3ms
04/17/2022 04:22:12
In this case, we have f(f(n)+f(0)) = n
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1
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720b617d6d7b48c2af76d73947bb18d3
193,692,307,453,771,780
Syst3ms
04/17/2022 04:22:27
So for any output, we can find a corresponding input, namely f(n)+f(0)
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help-10
720b617d6d7b48c2af76d73947bb18d3
193,692,307,453,771,780
Syst3ms
04/17/2022 04:22:35
By definition, it is surjective
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PuddinAru
04/17/2022 04:23:22
But in here k is independent of n right?
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720b617d6d7b48c2af76d73947bb18d3
943,069,425,274,339,300
PuddinAru
04/17/2022 04:35:17
.close
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87550ce8850841c3a686685d33d14546
406,811,109,522,407,400
Dávid
04/17/2022 04:39:48
Hi, can anyone help me? I don't know how to start 😄
https://cdn.discordapp.c…3534/unknown.png
unknown.png
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Limitless222
04/17/2022 04:59:03
Without working it out myself, I would start with working out the probability of getting two 6's in a row in 2 rolls. Then getting two 6's in a row on the third roll without getting it on the 2nd roll. I'd then either expect to see some telescoping sum or to realise that I have to work out the probability of not gettin...
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help-10
87550ce8850841c3a686685d33d14546
406,811,109,522,407,400
Dávid
04/17/2022 05:05:11
Let's say I have 3 throws, then there are two possible solutions, 6X6 and XX6. What are the chances of me throwing one of them? (1/6)*(5/6)*(1/6) + (5/6)*(5/6)*(1/6) = 5/36
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help-10
87550ce8850841c3a686685d33d14546
406,811,109,522,407,400
Dávid
04/17/2022 05:08:09
that's good?
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help-10
87550ce8850841c3a686685d33d14546
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Dávid
04/17/2022 05:13:23
Or I have to do all the possible combinations
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help-10
87550ce8850841c3a686685d33d14546
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Limitless222
04/17/2022 05:14:02
If X is a result that is not 6, your calculations are correct. Don't you want to find when there are two 6s in a row? So for two rolls, you're looking for exactly (6,6), which is (1/6)(1/6). For 3 rolls, we have (X,6,6) which is (5/6)(1/6)(1/6). For 4 rolls, (6/6)(5/6)(1/6)(1/6).
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help-10
87550ce8850841c3a686685d33d14546
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Dávid
04/17/2022 05:18:54
I have to calculate the probability of "ai" first. (does not fall twice 6 in a row and six fall in the last roll) Then the probability of "bi." (does not fall twice 6 in a row and six not fall in last roll) So then I can calculate it now as described.
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help-10
87550ce8850841c3a686685d33d14546
406,811,109,522,407,400
Dávid
04/17/2022 05:21:52
Then I have to find the generating function for a (x) and b (x) with a system of recurrent relationships
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help-10
87550ce8850841c3a686685d33d14546
396,015,145,131,835,400
Limitless222
04/17/2022 05:29:33
Your calculations look correct for ai for 3 rolls.
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help-10
87550ce8850841c3a686685d33d14546
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Dávid
04/17/2022 05:45:17
Thanks for the help 🙂
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Dávid
04/17/2022 05:46:17
.close
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ae4acc759aee453a8eab791110b6569d
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HimboKisser
04/17/2022 07:00:42
What do you do when two directional vectors aren't parallel and they intersect, how do you calculate that?
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help-10
ae4acc759aee453a8eab791110b6569d
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Limitless222
04/17/2022 07:02:29
Break them up into components.
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help-10
ae4acc759aee453a8eab791110b6569d
451,866,498,357,526,500
HimboKisser
04/17/2022 07:03:11
What do you mean?
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help-10
ae4acc759aee453a8eab791110b6569d
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theguy
04/17/2022 07:03:40
Do u want to calculate the point where they interesect?
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help-10
ae4acc759aee453a8eab791110b6569d
451,866,498,357,526,500
HimboKisser
04/17/2022 07:04:47
I'm unsure, to be honest. My teacher gave us this sort of map, what they are if they're parallel and if they're not. But we aren't at that point of just *what* to do if they intersect.
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help-10
ae4acc759aee453a8eab791110b6569d
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Kulsgam
04/17/2022 07:04:57
are you aware of vector equations?
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help-10
ae4acc759aee453a8eab791110b6569d
667,385,854,687,182,800
Kulsgam
04/17/2022 07:05:10
if 2 vectors intersect you can equate the vector equations
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help-10
ae4acc759aee453a8eab791110b6569d
667,385,854,687,182,800
Kulsgam
04/17/2022 07:05:22
and then find a common scalar product value
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