# Canceling Non-existent Limits

**Calculus**Level 1

**True or false**:

Because both the limits, \( \displaystyle \lim_{x\to\infty} \sin x \) and \( \displaystyle \lim_{x\to\infty} \cos x \) does not exist, then the difference of their limits must be equal to 0:

\[ \lim_{x\to \infty} ( \sin x - \cos x) = 0 \; .\]