Definition - Bhaskar 
              Shankara uses the word bAdha multiple times
                at various places...In ArambhaNAdhikaraNam (2-1-14)
                sUtra bhAshyaM Shankara in a single para uses
                this word several times to say that bAdha is
                nothing but sublation of
                wrong knowledge (bAdhitAnuvrutti
                or bAdhita mithyAj~nAna). It would be important
                here to note that Shankara alternatively, at
                some places uses the words like nAsha, laya etc.
                But these words also implicitly & contextually
                mean bAdha only...  
              The word bAdha can be explained with a simple
                example. If I see a synthetic snake, the first
                cognition of the 'snake' causes be fear, anxiety
                etc. After the detailed examination of the same,
                I get the knowledge that the snake is not real
                but it is mere 'synthetic' snake. But even
                after having the correct knowledge of the snake,
                the shape of snake does not disappear from my
                sight... but for me ONLY wrong
                knowledge of
                'real' snake will get sublated. Though I could
                see the curved snake with its broad hood in the
                front, sharp tail at the end, now I have the
                bAdhita j~nAna of this seemingly 'real' snake & with
                that bAdhita j~nAna of that 'real' snake, there
                is no more anxiety & fear to trouble me.  
              So, bAdhA or bAdha means when one knows/realizes
                the true nature of the object. Though it appears
                in all its (seeming) reality, one's realization
                would be that it is not real; it is mere false
                appearance & does not have actual existence.
                Shankara applies the same logic & says though
                brahma j~nAnI, like other loukika-s, sees this
                world, for him the knowledge of the seemeing
                reality of the world will get sublated with the
                real knowledge of Atman. He explains this beautifully
                in sUtra bhAshya (
2-1-14)
:  
              atashcha idaM shAstrIyaM brahmAtmatvaM
                  avagamyamAnaM svAbhAvikasya shArIrAtmatvasya
                  bAdhakaM saMpadyatE rajvAdhi buddhaya iva sarpAdi
                  buddhInAM, bAdhitE cha shArIrAtmatvE tadAshrayaH
                  samasthaH svAbhAvikO vyavahArO bAdhitO bhavati.  
              From the above, it may be noted that for a brahma
                j~nAnI too, there exists the jagat & he too
                sees the vyavahAra as others do, but the difference
                for him is that the seeming reality of the existence
                of the world has been sublated (bAdhita) by the
                really real, non dual nature of brahman. 
                
              Comment from Michael Reidy  
              It occurred to me in this discussion of bAdha/sublation
                that the prime examples of its working viz. dream
                and confusion, can have their own distorting
                effect. We need to distinguish between manner
                and matter, between the act of sublation and
                that which is being sublated. Because of the
                examples of sublation that are the analogy for
                the ultimate sublation happen to deal with the
                unreal, we may be nudged into thinking, that
                this relative state when sublated upon our achievement
                of a realisation of the absolute, will be likewise
                unreal, fantastical, and without substance. 
              As we have seen, bAdha stresses that the state
                that is sublated is not thereby annihilated but
                continues to exist, preserved if you like, with
                a different understanding of its nature. If we
                focus on the activity of sublation rather than
                the matter that is sublated then counter intuitive
                and incredible positions about the status of
                the world for the j~nAnI may be avoided. 
              This is the thinking behind the Tripura Rahasya's
                statement: 
               ..."I say that you do not understand the
                advaita shastra; nowhere do the sastras declare
                the jagat to be unreal. But yet they proclaim
                advaita to be certain. shruti-s such as "He
                became all", Only the non-dual Supreme Being
                shines as the universe", declare the jagat
                to be real and thereby non-duality is not impaired.
                Though the town reflected in a mirror seems distinct
                yet it cannot exist without the mirror and so
                is no other than the mirror; in the same manner
                the jagat though seeming distinct is no other
                than the Supreme Self. So non-duality is unimpaired." (pg.240) 
              Jagat is sublated on realisation. Our understanding
                of what it is alters radically. The acts of sublation
                that we are offered as analogies have as their
                matter dream and confusion but we ought not to
                let that fact alter our view of creation. What
                creation is for the j~nAnI is beyond the dichotomies
                of reason. 
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