Q:

Paradigmatic vs syntagmatic relationship

I was exploring some various aspects of corpus linguistics and studying different approaches to corpus research on the internet when I came across these phinomena of paradigmatic
and syntagmatic relations.  Can I get a satisfactory elucidation of both the concepts as well as how do the two technically and practically differ? 

A:

Paradigmatics
Paradigmatic relations are relations of opposition and functional identity of linguistic elements (“OR - OR”), i.e. the paradigm combines sets of linguistic units that are similar according to one, and opposed according to some other criterion(s).  Paradigmatics determines to which level of grammatical categoric hierarchy this or that language unit belongs, by analogy with units similar to it.  For example:

Phonemes b, ɪ, g, s, t are the building blocks of morphemes big and -est. 
Morphemes big and -est can combine to form the lexeme biggest. 
The lexeme biggest is a part of the sentence That's the biggest fish I've ever seen! 

Syntagmatics
Syntagmatic relations can be defined as relations of compatibility of elements of the level in a sequence of speech events, i.e. combination of phonemes with phonemes, morphemes with morphemes, etc.  Syntagmatics combines language units by their direct combination. 
The logical formula of syntagmatic relations is the formula "AND - AND", i.e. both one element and another element together, side by side, one after another, forming a chain of the same-order elements of a certain length. 
Examples of syntagmatic relationships:

b=ɪ=g=ɪ=s=t, bɪg=ɪst (phonetico-phonological level)
big=est, water=s, walk=ing (morphological level)
teach=er, re=name (word-building sub-level)
tall man, tall tree (lexical level)
The tree is tall. ( syntactical level)

