[Math] Are all integers fractions

Question

In a college class I was asked this question on a quiz in regards to sets:

All integers are fractions. T/F.

I answered False because if an integer is written in fraction notation it is then classified as a rational number. The teacher said the answer was True and gave me the link http://www.purplemath.com/modules/numtypes.htm. As a teacher of mathematics in the K-12 system I have always taught that integers were all whole numbers above and below zero, and including zero. All of the resources I have used agree to my definition. Please clarify this for me.

What is the truth, or are she and I just mincing words?

Answer 1

Integers are fractions, because a number is itself no matter how you write it.

A relevant section from Lockhart's A Mathematician's Lament:

In place of a natural problem context in which students can make decisions about what they want their words to mean, and what notions they wish to codify, they are instead subjected to an endless sequence of unmotivated and a priori “definitions.” The curriculum is obsessed with jargon and nomenclature, seemingly for no other purpose than to provide teachers with something to test the students on. No mathematician in the world would bother making these senseless distinctions: 2 1/2 is a “mixed number,” while 5/2 is an “improper fraction.” They’re equal for crying out loud. They are the same exact numbers, and have the same exact properties. Who uses such words outside of fourth grade?

Here's a relevant comic from SMBC: