Congruence (Number Theory)/Examples/1.6 congruent to 0.6 Modulo 1

Example of Congruence Modulo an Integer

$1 \cdotp 6 \equiv 0 \cdotp 6 \pmod 1$

Proof

\(\ds 1 \cdotp 6\)

\(=\)

\(\ds 1 \times 1 + 0 \cdotp 6\)

\(\ds \leadsto \ \ \)

\(\ds 1 \cdotp 6\)

\(\equiv\)

\(\ds 0 \cdotp 6\)

\(\ds \pmod 1\)

$\blacksquare$

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): congruence modulo $n$
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): congruence modulo $n$