Direct sum notation: $G = \bigoplus_{\alpha < \beta}\mathbb Zx_{\alpha}.$

Question

I was reading the direct sum of the groups and the index notation looks little bit strange for me.

Group $G = \bigoplus_{\alpha < \beta}\mathbb Zx_{\alpha},$ where $\beta$ be an ordinal. Is this group in the form $\mathbb Z\oplus \mathbb Z \oplus \mathbb Z \oplus ...,$ where the number of copies of $\mathbb Z$ is less than the cardinality of $\beta$ ?

Thank you.