I reply False due to the fact that if an creature is composed in portion notation that is climate classified together a reasonable number. The teacher claimed the answer was True and also gave me the connect http://www.purplekeolistravelservices.com.com/modules/numtypes.htm. Together a teacher of keolistravelservices.comematics in the K-12 mechanism I have constantly taught that integers to be all totality numbers over and below zero, and including zero. All of the resources I have actually used agree to my definition. You re welcome clarify this because that me.

What is the truth, or space she and also I simply mincing words?

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Zev Chonoles
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Integers room fractions, since a number is itself no matter just how you create it.

A pertinent section indigenous Lockhart"s A keolistravelservices.comematician"s Lament:

In location of a natural difficulty context in i beg your pardon students can make decisions about what they desire their words come mean, and also what notions they great to codify, castle are instead subjected to an countless sequence that unmotivated and also a priori “definitions.” The curriculum is obsessed v jargon and also nomenclature, seemingly for no other purpose than to carry out teachers v something to check the student on. No keolistravelservices.comematician in the world would stroked nerves making this senseless distinctions: 2 1/2 is a “mixed number,” when 5/2 is one “improper fraction.” They’re equal for crying out loud. They room the same precise numbers, and have the same specific properties. Who offers such words external of fourth grade?

Here"s a pertinent comic indigenous SMBC:


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I want to point out a various perspective. This is a common issue wherein non-rigorous usage of language leader to confusion. We frequently treat objects the are indistinguishable (under a maybe unspoken equivalence relation) together if they space equal.

Integers and rational numbers space not fractions, in the strictest feeling of words "are". Because that example, the fractions $1/1$, $4/4$, and $8/8$ room all different fractions, however they all represent the exact same integer. (Actually, I have to say "the fractions represented by the expression $1/1$, $4/4$, and also $8/8$.") none of the fractions $1/1$, $4/4$, and also $8/8$ accurate is the creature 1. If they were every the exact same as the creature $1$, they would all it is in the exact same as each various other - however they room not, since they are various fractions. What is true is that they have the very same value as each other.

Similarly, the fountain $1/2$ and also $2/4$ room not both the same as the rational number $1/2$, because they space not the very same as every other, because they have various numerators. That would insurance claim that a rational number has a numerator?

When us write$$1 = 4/4 = 8/8 $$the "equals" over there only means that fractions represent the very same number (they have the same value), no that they are the same fraction. In various other words, the $=$ we write is actually an equivalence relationship on a set of fountain - the equivalence relation gift "has the very same value". We have no symbol the we generally use to denote "actual" equality the fractions. This suggest is often ignored completely in lower-level texts.

The an initial place that human being start to think about these points in detail is in abstract algebra. In the context, we run into plenty of interesting distinguish that would not be visible in elementary keolistravelservices.com. For example, under the interpretations in many algebra books, $keolistravelservices.combbZ$ is an extension of the semigroup $keolistravelservices.combbN$ to a group; $keolistravelservices.combbQ$ is the field of fountain of $keolistravelservices.combbZ$; and $keolistravelservices.combbR$ is the Dedekind perfect of $keolistravelservices.combbQ$. It complies with from these interpretations that the organic number 1 is not the very same as the creature 1, both are various than the reasonable number 1, and also all 3 of those are different from the genuine number 1.