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The real numbers $\mathbb{R}$ with the following three binary operations:

• The maximum: $(x,y)\mapsto\max\{x,y\}$.

• The sum: $(x,y)\mapsto x+y$.

• The product: $(x,y)\mapsto x\cdot y$.

The maximum is to the sum what the sum is to the product, except from for the fact that the maximum does not have inverses, nor a unit, i.e. $(\mathbb{R},\max,+)$ is a semiring, while $(\mathbb{R},+,\cdot)$ is a ring.

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The real numbers $\mathbb{R}$ with the following three binary operations:

• The maximum: $(x,y)\mapsto\max\{x,y\}$.

• The sum: $(x,y)\mapsto x+y$.

• The product: $(x,y)\mapsto x\cdot y$.

The maximum is to the sum what the sum is to the product, except from the fact that the maximum does not have inverses, nor a unit, i.e. $(\mathbb{R},\max,+)$ is a semiring, while $(\mathbb{R},+,\cdot)$ is a ring.