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Description
Counterexamples in Probability: Third EditionMost mathematical examples illustrate the truth of a statement; conversely, counterexamples demonstrate a statement's falsity if changing the conditions. Mathematicians have always prized counterexamples as intrinsically enjoyable objects of study as well as valuable tools for teaching, learning, and research. This third edition of the definitive book on counterexamples in probability and stochastic processes presents the author's revisions and
Most mathematical examples illustrate the truth of a statement; conversely, counterexamples demonstrate a statement's falsity if changing the conditions. Mathematicians have always prized counterexamples as intrinsically enjoyable objects of study as well as valuable tools for teaching, learning, and research. This third edition of the definitive book on counterexamples in probability and stochastic processes presents the author's revisions and corrections in addition to a substantial new appendix.Suitable as a supplementary source for advanced undergraduates and graduate courses in the field of probability and stochastic processes, this volume features a wide variety of topics that are challenging in both content and detail. The text consists of four chapters and twenty-five sections. Each section begins with short introductory notes of basic definitions and main results. Counterexamples related to the main results follow, along with motivation for questions and counterstatements that range in difficulty. A familiarity with basic notions and results in probability and stochastic processes is assumed, and a chapter of supplementary remarks provides a wealth of information about original sources as well as references for further studies.
Binding Type: Paperback
Publisher: Dover Publications
Published: 01/15/2014
ISBN: 9780486499987
Pages: 400
Weight: 1.00lbs
Size: 8.40h x 5.50w x 1.00d
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4.9 ★★★★★
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★★★★★ 5
Tighten the compression nut
Color: Tan, Color: Tan
My cat loved this groomer right out of the box! She was so aggressive, though, that the brush kept coming out of the base. When my husband got home from work, I asked if he could put some kind of glue in it. Two minutes later, he had it fixed. He says this is a compression nut that you tighten with your fingers (a wrench would probably break it) on to the metal ends of the brush. The look on his face said what he didn't dare say out loud. In my defense, there were no instructions included.
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Reviewed in the United States on April 3, 2022
★★★★★ 4
Cat likes it
Color: Tan
My cat doesn't use it a lot but when she does she seems to like it
WAS THIS REVIEW HELPFUL?YesReportShare
Reviewed in the United States on May 13, 2026
★★★★★ 3
Product seems fine. My cats won't use.
Color: Tan
My cats won't use this or go anywhere near it. I am considering taking the brush part off the base and trying to attach it to some furniture they constantly rub against. The arch has to be assembled, which was super easy. The brush is sturdy and the base holds it well. I am keeping it in hopes of finding some way to teach my cats how great it could feel. The 3 stars rating is strictly because my cats won't use the product, so that lowers it's value for me.
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Reviewed in the United States on December 2, 2022
★★★★★ 1
Broken right away … nonfunctional
Color: Tan
Hi, all, I bought this item back in 2023. The idea is great, as we all know cats love to rub against scratchy things. The first thing that I’ve noticed is that the bristles were too soft. The devil is in the details, as they say and the execution of this piece needs to be addressed. My cats broke it in 1 day; the base of the wire was torn out of platform. I should have returned it right away, but I thought that I can fix it by glueing back together. Two years and multiple attempts after, it is nonfunctional. In its current disposable state, the price should be around 6-7 $. Connection of wire to the base needs to be reinforced by the manufacturer to make a good product!
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Reviewed in the United States on January 31, 2025
★★★★★ 5
Buy this right now. DO IT! Did you buy it yet? You should.
Color: Tan
Let me Begin by saying that our cats have a lot of enrichment. They have a lot of toys, we keep the windows open, they have their own freaking Fountain and they sleep in our bed. But let me tell you about this cat scratcher.
When they say that they enjoy it, I mean that day love it! It's their favorite thing in our entire house. Anytime I come home from work or from a night out or anyting, one of the cats is lying on this scratcher.
We originally bought it for our cat Reintte's birthday, and while it was easy to put together the bottom tines came out of the holes pretty easily, so I used to hot glue gun, put a drop in each spot, and it's been holding up for 2 years.
My cat is actually obsessed with this. It's her favorite thing in the entire world, I think she likes it more than she likes me. I cannot recommend this enough. As a crazy cat mom, I am very particular with the toys and treats and enrichment that I get for my girls, and especially for Reinette who has a lot of extra needs, and she uses it every day. I mean EVERY. DAY. Sometimes we get toys or beds or trees for the cats that they don't use until we move them somewhere that they realize oh hey I like it in this spot, wherever we put this scratcher, books of the girls will find it and use it immediately. If I can't find one of the cats, I'll just rub my handle on it and the sound that it makes will call them to me. It's astounding.
Even my cat that doesn't like to be brushed loves this scratcher. I bought it for a ranette because she loves being brushed and she steals my hair brushes and she brushes her face on them by herself so it was a perfect gift for her, but our other cat you can't come near her with a brush. She gets so upset and angry that it's really difficult to brush her. And she loves this scratcher.
Just buy it. Buy it now. I'm not even kidding. It's amazing.
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Reviewed in the United States on July 11, 2019
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