# Last element in the world

**Discrete Mathematics**Level 4

Let \({ A }_{ 1776 }\) be the set \(\left\{ \dfrac { 1 }{ 1 } ,\dfrac { 1 }{ 2 } ,\dfrac { 1 }{ 3 } ,\ldots ,\dfrac { 1 }{ 1775 } ,\dfrac { 1 }{ 1776 } \right\}\).

Remove any two elements, say a and b, from \({ A }_{ 1776 }\), and replace them with the single number \(ab+a+b\) to form set\({ A }_{ 1775 }\). Continue in this manner, until you have performed \(1775\) such operations, to form set \({ A }_{ 1 }\), which contains a single element.

What is this last element?