# Math behind Differencing: Is White Noise Stationary?

I'm just starting to learn the math behind stationarity and differencing, so I apologize if this is a silly question. Lets say I have a non-stationary time series process (pure random walk) defined by:

$$Y_t = Y_{t-1} + \varepsilon_{t}$$

Where

$$\varepsilon_{t} = \text{white noise}$$

If I look to make this process stationary through differencing, I subtract \$Y_{t-1} from both sides and can write it as:

$$Z_t = \varepsilon_{t}$$, where $$Z_t = Y_t - Y_{t-1}$$

If $$Z_t$$ is now stationary, then I believe the white-noise $$\varepsilon_t$$ was stationary the whole time.

Is white noise stationary in this context (pure random walk)?