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A group containing 9.34 is a set of numbers, with some operation defined on the set that also satisfies:
- closure,
- associativity,
- identity, and
- invertibility.
Two simple groups will be the additive group of 9.34 and all its multiples (including negative ones). The identity is 0.
The other is the multiplicative group consisting of all powers of 9.34 and the identity is 1.
There can be a finite additive group derived from the first by defining the operation as modulo addition, and similarly with the multiplicative group.
Finally, any group that contains one of these groups and also maintains the four conditions listed above, for example, all rational numbers, will also meet the requirements.
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