Rational Numbers form Subfield of Real Numbers
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Recall that Rational Numbers form Ordered Field.
Then from Rational Numbers form Subset of Real Numbers:
- $\Q \subseteq \R$
Hence the result by definition of subfield.
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $4$: Fields: $\S 16$. Subfields: Example $21$
- 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): $\S 2.1$: Subrings: Examples $1$
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $3$: Field Theory: Definition and Examples of Field Structure: $\S 88$