infimum and supremum

[wooden hawk]

Great people please help on this

[wooden hawk]

Please any help 🙏

[thorny sage]

Do u understand the statement u have to disprove

Like really understand

[wooden hawk]

Looks tricky somehow

I think we would just make a counterexample using any real number >= 1

@thorny sage pls if you can interpret the statement clearer

[thorny sage]

A quick example. Let’s say one sequence takes a maximum at 1 at n=35 and another sequence takes a max at 5 at n=12. Then when adding up the two sequence specific to their index so for example sequence one and sequence two at n=12 is prob not gonna be 1+5 and at n=35 the same since u only viewed one sequence specifically.

[wooden hawk]

Yes I get the example
That's true

[thorny sage]

So we can use this logic on this example

Since the one sequence takes it sup at n even

And the other one at n=1

Therefore added they will be 2, but if u add them before it can only be 1.5 showing the inequality