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hey welcome everybody

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tune in next lecture of from some
programming 101 axe

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today we're going to talk about list
comprehension

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and this comprehension siege are

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a mechanism to write code that
manipulates collections

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and and every look at most programming
languages

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most of the features in a programming
language

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has to do wit dealing with collections
if you look like

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a traditional imperative language
judge's job our C sharp

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an it has a wide range of mechanisms to
deal with connection

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form the while loops do while loops

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foreach loops contain you break

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and all these constructs are there to

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it to rate over collections and

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now of course mathematicians have been
dealing with collections

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an for for centuries and

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and for mathematicians the favorite

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collection type is sets and

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sets however are computationally a
little bit awkward

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because when you have a set image that
duplicated

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elements are removed which implies that
you need a quality to delete chechan

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especially in a functional language like
has gone

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and it's very hard well and possibly
have to solve the halting problem

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2d decide equality between functions

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so what

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haskell did it took some of the ideas
that meant mission mathematicians have

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used

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for a long time to deal with chats and

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simplified them to work over lists
analysts are

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my favorite collection died and and the
reason is delish

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just gives you didn't bare minimum to
deal with the collection

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you can as you have seen if we have a
list that's composed out of a hat and a

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tail

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you can decompose that less recursively
but just picking off the first element

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one by

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well and that's very convenient and
short bridge

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very few restrictions on the collection
time

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unless statuary how are you issue
quality of the elements or a race where

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you assume

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am constant I'm indexing so Schatz

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are in some sense the most your form

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of collection types and the job on a job
for eight

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day am gold these lists streams

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and to emphasize dejar

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collections where you can only
xsd:element

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one by one and in that sense

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has call lists are an example of a job
for eight streams in that philosophy

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alright thats

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and look at how mathematicians to use

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so-called set comprehension to define
sets

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and here's an example a.m. a base at

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dead it sits at the mall squares an

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which and values

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between one and five show is its X
where'd

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where axe is from this they confirm this
at 125

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so the result of this is dis at 149 1625
and

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but as i sad I'm every take

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ax to range over functions then this
becomes really hard to implement

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so what people dead and

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in functional languages is take the same
notation the same ideas

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but instead of sets usual ish and show
SATCOM branches for mathematics

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become list comprehension and Haskell

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and here's that same example region as a
list comprehension so here you see

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it's the list of square numbers

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X square to wear action is taken from
the list

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want to fight a year you see this year
redesigned axe

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is taken from the less than 125 and

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if you evaluate this you will see that

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this returns the list 1 for 9 16 25

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but is alleged not set

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the expression

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X taken from want to buy that's called a
generator

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an and the reason it's called a
generator because it

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defiance on how to generate value Sh

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Forex writer axis taken from that shit

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I'm of course answers everything

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and has call and AR that's a good

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aspect of programming language has to be
compositional so you should be able to

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just you know recursively use the same
structures over and over again

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and comprehension scan have multiple
generators

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and here you see an example of that

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so we attic all pairs x-com I Y

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Rx is drawn from one to three and why

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is drawn from for Fife and what you see

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is dead the why various

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faster then DX show the result list is

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14 15 to

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425 3435 an

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as another way to look at ID snatched it

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generators are multiple generators is
like

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and nested loop where do why is the NRA
nope

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and the axe is the outer loop so if we
change if we show up the order of the

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generator

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then now and X

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very smart witty biggest this becomes
the envelope so what we get now

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is am but notice that we still

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have here extra mile i show we only show
up the order

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of the generators not the order of the
very most

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so now instead of an and

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this guy moving fast as you get

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X moving fast so the result is 14

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two for 34 et cetera and

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and this notion of generators

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an you will recognize dead

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in many many programming language
showing haskell these are less go

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branches if you use by Tom

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and also as list comprehension an

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skyline has forgone branch ins at sharp
edge comprehension

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and C sharp in Visual Basic an

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half as link comprehension

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am and if you look at the language like
she call

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which is completely built and on top of
comprehension

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only dare you don't ride em this concise
a year deride select from where

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a jet dry but it's basically the same
idea so by studying

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and let's go branches and has gone you
will be well equipped

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to use the same ideas in whatever
language you encounter them in

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alright and

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now

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we have seen now a few simple examples
for generators

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where the generators only had Constance
but

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generators can also deep and on each
other

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and just like when you have a nope inner
loop

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can use variables from the outer nope
and Red Gum branches

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that's no different show every look here

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we say pictures drawn from wanted three
and then

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why is drawn from X 23

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so axes and scope in the generators that

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gone after it and every executed dis
comprehension

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we get the latest an one long

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ego-c I Y is drawn from one to three

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because action starts out and wong so we
get 11 12 13

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than an why is exhausted show

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we're going to checked the next value
action that will be too

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so now why is taken from two to three so
easy to

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to 23 and then the last iteration

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we take xtube eatery and then why is
drawn from the list

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323 shown at is the last value is just

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3 comments re am but again your

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totally familiar read this because this
is the same and how nested loops work

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and any language showed the inner loop
can

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use variables defined and outer loops

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and one of the nice things

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of comprehension and especially of and
the band generators

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is that you can ride very concise God

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for example an if we want to take a list
of lists

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and flatten them into a single list an

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we can do that an with the following
comprehension

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so each day just give me every list
out-of-date lists of lists

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and then just give me every element of
that list

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and return that so this is a at EE
nested loop that goes over

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every last in this list a blessed and
just

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yields all the values to return

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a single-edged of type a up the same
element type

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as the originally saw by me

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and concatenate 123 45 and six

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the result will be on 23 456

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right Jul very very

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gone size code and that we can ride
using comprehension now the next thing

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this I generators that you want to use
in a comprehension and that's also

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and use a lot inset comprehension is to
allow filters

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you want to and you now

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have X drawn from some collection

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but you want to draw out certain values

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forage a predicate does not hold over
job but we want to have

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all the even numbers between one and 10

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we can just say drawing X is drawn from
wanted an

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and filter out only the even numbers so
the result

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of this is a list 246 aids done

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the even numbers between long and then

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and and its sequel you will recognize
this as a select where

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so the WHERE clause here an is called a
guard

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in ask our and if you use a link

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and list comprehension czar and
comprehension syntax debt will be also

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be called

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where

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here's a am

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example an that uses guards to take

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number and break it down into its
factors

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so what are the factors well we take a
number and

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we take all the numbers between 1 and
then

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an and then recheck we only

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retained oesch forage and modulo
actually 0

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so defectors were 15 sure we start out
with all the numbers between

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1 and 15 and then we'd throw out all the
numbers

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for rich it and modulo axe is not here
are

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and in this case defectors are 13 5 and
fifty

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and then we can use this

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factors an function

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to defined a very simple

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am predicate to check whether numbers
prime

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numbers prime if defectors have that
number are exactly the list Wong and an

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and for jon bon five is not a prime

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because defectors are not just one and
fifteen

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as one three five 10 15 but seven

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is a prime because you can check by
using Ghei are your

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on favorite programming language that
defectors are seven are one and seven

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and so we decide that

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7 as a prime okay

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so everyone to not check whether

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an in our what are the primes up to a
certain number

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well weekend ride this simple let's go
branches are we say

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give me all the numbers between two and
then were and that's the brand matter to

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dish

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function and then I only want to can't
maintain the prime numbers I filter out

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all the numbers that are not branch over
I want to have

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all the prime numbers and up to 40

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an I just run this and list
comprehension

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and I get an all the prime numbers now
of course this is not the most efficient

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way

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to compute prime numbers but I think
it's a very nice illustration

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views English comprehension so see you

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and the next chapter