2. We shall be dealing with vector spaces over either the reals or the complex numbers.
我们应处理向量空间超过要么雷亚尔或复杂的数字。
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3. The supremum axiom of the reals refers to subsets of the reals and is therefore a second-order logical statement.
实数集的上确界公理用到了实数集的子集，这是一种二阶逻辑的陈述。
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4. The kicker: Most of Bündchen’s paychecks are paid in euros and Brazilian reals, resulting in an increase in earnings versus the dollar.
注：邦辰大部分收入是以欧元和巴西货币雷亚尔支付，因此按照汇率兑换成美元后数额更大。
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5. In addition, by using inactivity time to characterize the second-price closed-seal auction rent, we investigate how the variation of the auction rents reals that of populations.
6. Mathematicians are familiar with this; common problems in algebra are more tractable when considered over the complex numbers than over the reals, even though complex arithmetic is more difficult.
7. Mathematicians are familiar with this; common problems in algebra are more tractable when considered over the complex numbers than over the reals, even though complex arithmetic is more difficult.
