In group theory, a branch of abstract algebra, an **infinite group** is a group that contains an infinite number of elements. In other words, if the cardinality (size) of the group is not a finite number, then the group is classified as infinite. Infinite groups can be categorized into various types based on their structure and properties.
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An infinite group is a group with infinitely many elements. An element of infinite order proves that its group is infinite, but the converse need not hold: an infinite group can have all elements of finite order.