Concatenating Lists: Associative but Not Commutative/Idempotent

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SUMMARY

The discussion clarifies that list concatenation is an associative operation but not commutative or idempotent. Given lists A = "abcd" and B = "1234", the concatenation results in AB = "abcd1234", demonstrating associativity through the equation (AB)C = A(BC). However, the commutative property fails as AB ≠ BA, exemplified by AB = "abcd1234" and BA = "1234abcd". The discussion emphasizes the importance of understanding these properties in the context of list operations.

PREREQUISITES
  • Understanding of list data structures
  • Familiarity with the concepts of concatenation and string manipulation
  • Knowledge of mathematical properties: associative, commutative, and idempotent
  • Basic programming skills to implement list operations
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  • Explore the differences between associative and commutative operations in programming
  • Learn about idempotent operations in functional programming
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Kenan1
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Hallo guys,
I'm looking for your help :). Here is a question from an Assigment, that i should tomorrow gave.

Explain that the concatenation of lists is associative but not commutative and not idempotent. (In this respect, there is one thing in common, however, two differences from the union.) Use as a symbol for the concatenation
K..L for lists K and L.
Thanks in Advance!
 
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Do you understand what "concatenation", "associative", and "commutative" mean? Given two lists, say A= "abcd" and B= "1234" their "concatenation" is AB= "abcd1234".

An operation is "associative" if (AB)C= A(BC). The differences are that, on the left, we combine A and B first, then add C to that. On the right, we combine B and C first, then add A to that.

An operation is "commutative" if AB= BA. That is, it does not matter which we have on the left and right.

Suppose A= "abcd" and B= "1234". Then AB= "abcd1234" and BA= "1234abcd". Are those the same string? Is concatenation "commutative"?

Suppose A= "abcd", B= "1234", and C= "x5y9z". Then AB= "abcd1234" so (AB)C= "abcd1235x5y9z" while BC= "1234x5y9z" so A(BC)= "abcd1234x5y9z". Are those the same string? Is concatenation "associative"?

- - - Updated - - -

Do you understand what "concatenation", "associative", and "commutative" mean? Given two lists, say A= "abcd" and B= "1234" their "concatenation" is AB= "abcd1234".

An operation is "associative" if (AB)C= A(BC). The differences are that, on the left, we combine A and B first, then add C to that. On the right, we combine B and C first, then add A to that.

An operation is "commutative" if AB= BA. That is, it does not matter which we have on the left and right.

Suppose A= "abcd" and B= "1234". Then AB= "abcd1234" and BA= "1234abcd". Are those the same string? Is concatenation "commutative"?

Suppose A= "abcd", B= "1234", and C= "x5y9z". Then AB= "abcd1234" so (AB)C= "abcd1235x5y9z" while BC= "1234x5y9z" so A(BC)= "abcd1234x5y9z". Are those the same string? Is concatenation "associative"?

- - - Updated - - -

Do you understand what "concatenation", "associative", and "commutative" mean? Given two lists, say A= "abcd" and B= "1234" their "concatenation" is AB= "abcd1234".

An operation is "associative" if (AB)C= A(BC). The differences are that, on the left, we combine A and B first, then add C to that. On the right, we combine B and C first, then add A to that.

An operation is "commutative" if AB= BA. That is, it does not matter which we have on the left and right.

Suppose A= "abcd" and B= "1234". Then AB= "abcd1234" and BA= "1234abcd". Are those the same string? Is concatenation "commutative"?

Suppose A= "abcd", B= "1234", and C= "x5y9z". Then AB= "abcd1234" so (AB)C= "abcd1235x5y9z" while BC= "1234x5y9z" so A(BC)= "abcd1234x5y9z". Are those the same string? Is concatenation "associative"?
 

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