Complete lattice and Bounded lattice

Question

Is every  Bounded lattice Complete  ?

Eg : ( { x : 0<=x<= 1} ,  <= )

This lattice is bounded , but is it complete ?

(I have a doubt ; what if we consider  irrational no.s as well)

Comments

A poset is called a complete lattice if all its subsets have both a join and a meet. In particular, every complete lattice is a bounded lattice

but not vice versa

See we can apply it for any number

as we can take p,q,r as elements of lattice

Now take p,q, r value as complex. irrational anything

But ans not change

---

@srestha mam . . U mean to say that suppose complex no.s are incomparable so they main not have a join or a meet

---

@VS

Complex number are not incomparable always

I think need not to research more on this

As complex number lattice will not come in GATE

---

@srestha mam

Thanks