Sequences

At the end of the last chapter it was pointed out that when processing set structures we are not concerned with the order in which elements are stored or accessed. Frequently, however, the ordering is significant; thus character strings are more than sets of characters — the ordering is vital <math display="block"><mrow><mo>&#x2019;</mo><mi>t</mi><mi>e</mi><mi>a</mi><mo>&#x2019;</mo><mo>,</mo><mo>&#x2019;</mo><mi>e</mi><mi>a</mi><mi>t</mi><mo>&#x2019;</mo><mo>,</mo><mi>a</mi><mi>n</mi><mi>d</mi><mo>&#x2019;</mo><mi>a</mi><mi>t</mi><mi>e</mi><mo>&#x2019;</mo></mrow></math> $$ 'tea', 'eat', and 'ate'$$ are all distinguishable as strings whereas <math display="block"><mrow><mo stretchy="false">(</mo><mi>t</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>a</mi><mo stretchy="false">)</mo><mo>,</mo><mo stretchy="false">(</mo><mi>e</mi><mo>,</mo><mi>a</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><mi>a</mi><mi>n</mi><mi>d</mi><mo stretchy="false">(</mo><mi>a</mi><mo>,</mo><mi>t</mi><mo>,</mo><mi>e</mi><mo stretchy="false">)</mo></mrow></math> $$ (t,e,a),(e,a,t)and(a,t,e) $$ are equivalent as sets.