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Description
The Real Number SystemConcise but thorough and systematic, this categorical discussion of the real number system presents a series of step by step axioms, each illustrated by examples. The highly accessible text is suitable for readers at varying levels of knowledge and experience: advanced high school students and college undergraduates as well as prospective high school and college instructors. The abundance of examples and the wealth of exercises more than 300, all with
Concise but thorough and systematic, this categorical discussion of the real number system presents a series of step-by-step axioms, each illustrated by examples. The highly accessible text is suitable for readers at varying levels of knowledge and experience: advanced high school students and college undergraduates as well as prospective high school and college instructors. The abundance of examples and the wealth of exercises--more than 300, all with answers provided--make this a particularly valuable book for self-study.The first two chapters examine fields and ordered fields, followed by an introduction to natural numbers and mathematical induction. Subsequent chapters explore composite and prime numbers, integers and rational numbers, congruences and finite fields, and polynomials and rational functions. Additional topics include intervals and absolute value, the axiom of completeness, roots and rational exponents, exponents and logarithms, and decimal expansions. A helpful Appendix concludes the text.
Binding Type: Paperback
Publisher: Dover Publications
Published: 09/12/2018
ISBN: 9780486827643
Pages: 240
Weight: 0.75lbs
Size: 8.90h x 6.00w x 0.50d
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4.1 ★★★★★
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★★★★★ 5
Great gift and great products
Size: 4 Piece Set
Bought this as a Christmas gift for my man and he absolutely loved it!
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Reviewed in the United States on June 8, 2025
★★★★★ 4
Not that Jack Black!
Size: 4 Piece Set
I bought this set assuming it was the actor/musician Jack Black’s skincare line. I figured a bearded celebrity would know all about quality beard care products. But actually it is not even named after a real person, it’s just a brand name. In fact, Jack Black the celebrity said he tried Jack Black products and they gave him a rash! Not a big deal though. I haven’t had such a reaction. The products smell fine, not overbearing, and seem to be working well. Cons: not exactly economical since it’s very small tubes. The beard oil pump is easy to overdo— Press too hard on the pump and you’ll end up with too much oil on your hands. A little goes a long way.
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Reviewed in the United States on February 13, 2024
★★★★★ 5
Wash/lube is travel/mini size
Size: 4 Piece Set
Did not realize beard lube and wash are mini/travel size but that’s my fault for not checking.
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Reviewed in the United States on May 3, 2026
★★★★★ 5
Never have I felt my beard this soft after using this beard oil…
Size: 4 Piece Set
I’m usually not the dude to leave a review on a product, but the second I hop out of the shower and tried the beard wash and beard oil, I was shocked.
Out of all the other beard oils and beard wash products i’ve used, this has to be the best result so far.
For the price, It can be expensive, sure. But it’s the only one you need. I don’t think i’ll ever go on a search for beard oil or wash ever again. This product is great!
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Reviewed in the United States on October 29, 2022
★★★★★ 3
SOME WHAT OK
Size: 4 Piece Set
IT WAS A GIFT, IT WAS SOME WHAT SMALL.
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Reviewed in the United States on August 19, 2025