## ATM Withdraw Cash – Use Case

Use Case Description: Allows any bank customer to obtain cash from their bank account. This use case begins when an ATM customer chooses a type of account from which the cash is to be withdrawn (e.g. checking) from a list of possible accounts, and to choose a dollar amount from a list of possible amounts. The system sends the transaction to the financial system for verification. If the financial system approves the transaction, the machine dispenses the appropriate amount of cash and issues a receipt. The dispensing of cash is also recorded in the ATM’s log.

## Cardinality of real numbers and set of real numbers between 0 and 1

Question : Show that the set of all real numbers has the same cardinality as the set of real number between 0 and 1.

Solution : Solution Let S be the open interval of real numbers between 0 and 1

S={x  ∈ R| 0 < x < 1 }.

Imagine picking up S and bending it into circle as shown below. Since S does not include either endpoint 0 or 1, the top-most point of the circle is omitted from the drawing.

## Comparison of Dijkstra’s algorithm and Floyd–Warshall algorithm

Floyd-Warshall Algorithm

Stephen Warshall and Robert Floyd independently discovered Floyd’s algorithm in 1962.

The algorithm solves a type of problem call the all-pairs shortest-path problem. Actually, the Warshall version of the algorithm finds the transitive closure of a graph but it does not use weights when finding a path.  The Floyd algorithm is essentially the same as the Warshall algorithm except it adds weight to the distance calculation.