Question

Determine if the subset f(x)=c , the set of all constant functions is a subspace of all continous functions

Answer 1

sure seems that way to me
c+d=e
another constant
a*c=ac
another constant

so I think it is closed under addition and multiplication

Answer 2

or a*c=d
however you want to write it...

Answer 3

okkie dokkie

Answer 4

I have one more lol

Answer 5

wait I totally misunderstood that question :/

Answer 6

ohh lol

Answer 7

I thought constant functions lol

Answer 8

I mean, wait...
no that is what they mean, right?
if constants are a subset of continuous functions?

Answer 9

i think so that is what i thought

Answer 10

ok then I'm right after all
sorry, other question?

Answer 11

umm when f(0)=1

Answer 12

umm that means that c=1

Answer 13

no?

Answer 14

talking about the same problem?

Answer 15

yes like instead of it being f(x)=c it is f(x)=1

Answer 16

whoops f(0)=1

Answer 17

f(x)=c
it doesn't matter what x is, c is whatever we choose it to be

if you mean a different problem, like asking about if f(0)=1 is a subspace of c, the answer is no

Answer 18

noo ok let me rephrase the question

Answer 19

Determine if the subset f(0)=1 is a subspace of all continous functions

Answer 20

now that i am looking at it i think the answer wld be yes

Answer 21

that is what I meant by if f(0)=1 is a subspace of c
ask yourself this:
what would be f(0)+g(0) in this vector space ?

Answer 22

c+d which is a constant which is a straight line. so it wld still be continous

Answer 23

but\[f(0)+g(0)=1+1=2\neq1\]

Answer 24

the question is not whether the result of our addition is in c, but whether it is in our subspace W

Answer 25

ohhh ok just digesting that

Answer 26

if the space is not closed by addition and scalar multiplication it is not a subspace, not matter if the result is in the original space V

Answer 27

like if it was f(0)=0 then it wld be a subspace right?

Answer 28

Right

Answer 29

kkk got it Thanks turing, U r a lifesavor

Answer 30

that, by the way, is called the null space
it is a subspace of every vector space

Answer 31

oh cool

Answer 32

sorry it's called 'zero space'*

Answer 33

null space is something else

Answer 34

every vector space has at least two subspaces
1)the zero space
2)itself

and it must be closed in /itself/
hope that helps

Answer 35

yes i am sord of getting the hang of it

Answer 36

glad, good luck :D

Answer 37

thanks