Can someone point me in the right direction?

[frank789]

Hi all! Down to the last question I couldnt get on my proofs homework...I just dont understand where to start with this one!

For all x in R, if there exists m in (0,inf), for all a in (0, inf), x<ma then for all b in (0, inf) x<b

Can I say,

If x<ma, and b is b+ma, (b>0, ma>0 by definition, so b+ma is in the interval (0,inf))

then by transitory property if x<ma<b+ma then x<b?

I'm sorry im wicked confused by how to prove this. I mean its really obvious that this is a true statement and I think thats messing me up as if a number is less than any number in an interval, then obviously its less than another any number in that interval.

A push in the right direction would be awesome!

Thanks
p.s. I was unsure which forum to post this in. Which should I have?

Edit:

Can I say,

Suppose ma<=b then b still has it's full interval
then since x<ma<=b, x<b?

I just feel like thats not enough or im missing something/doing something wrong

 

[Steven G]

Hi all! Down to the last question I couldnt get on my proofs homework...I just dont understand where to start with this one!

For all x in R, if there exists m in (0,inf), for all a in (0, inf), x<ma then for all b in (0, inf) x<b

Can I say,

If x<ma, and b is b+ma, (b>0, ma>0 by definition, so b+ma is in the interval (0,inf))

then by transitory property if x<ma<b+ma then x<b?

I'm sorry im wicked confused by how to prove this. I mean its really obvious that this is a true statement and I think thats messing me up as if a number is less than any number in an interval, then obviously its less than another any number in that interval.

A push in the right direction would be awesome!

Thanks
p.s. I was unsure which forum to post this in. Which should I have?

Edit:

Can I say,

Suppose ma<=b then b still has it's full interval
then since x<ma<=b, x<b?

I just feel like thats not enough or im missing something/doing something wrong

I am a bit confused when you say b is b + ma. To me that means b = b + ma which is only true if ma=0 and you do not want ma = 0.

If I understand what the theorem states (and I make no promises that I do), the theorem will follow if we can show that ma<b. (if x<ma and ma<b, then x<b).
So you are given a and b and must find m. Is there a theorem that you were taught that shows that such an m exists? Which course are you taking? Is it real analysis or basic algebra? We really need to know this.

To answer your question regarding where to post this problem it really depend on which course you are studying.

 

[frank789]

its for a intro math proofs course. I have a solution deemed acceptable that i understand

sorry for the confusion and thanks for the help

 

[Steven G]

its for a intro math proofs course. I have a solution deemed acceptable that i understand

sorry for the confusion and thanks for the help

I reread the statement of the theorem and it is very confusing to me. Can you maybe rephrase it.