what are the integer numbers?

Question

what are the integer numbers?
what ist he smallest integer?
what is the largest integer?
what determines if an integer is odd or even?

Answer 1

Think of a line that has 0 at its middle and runs forever in both directions. This is the NUMBER LINE, and all Real Numbers can be found on it.
to minus infinity...__-3__-2__-1__0__1__2__3...to infinity

Whole Numbers are (0,1,2,3,4....) there are no fractions included. Often the set of Whole Numbers is called the counting numbers. You can hold up 0-10 fingers. With the help of your friends you can hold up even more. But, you can’t not hold up a finger, then it becomes zero. So the set of Whole numbers doesn’t contain any negative numbers. You can’t hold up 3/32 of a finger so the Whole numbers don’t have any fractions. (Sure you can hold up 1/3 or maybe ½ a finger, but you can’t hold up ¾ of a finger and you can’t hold up 0.1 fingers.)
Integers are all the Whole numbers and the negative numbers.
Integers are this set: (...-3,-2,-1,0,1,2,3...) again there are no fractions.
This makes the set of the Whole numbers a subset of the set of Integers.
So the number line that I created above is the set of Integers, with each Integer being a number that I showed.
The smallest Whole Number is 0.
The smallest Integer can't be 0, because zero is in the MIDDLE of the number line. For every number you can think I can subtract one from it and get a smaller number or I can add one to it and get a larger number. I can do this until the end of time, or until INFINITY.
Therefore the Largest Whole Number is infinity. The Number line runs in both directions and it goes on forever in both directions. Therefore the largest Integer is infinity and the smallest Integer is minus (or negative) infinity. (Remember that zero is in the middle of the number line).
What about all the other numbers like 21 1/2 or 5/32, or 3.14159?
These are the numbers that fall into the __ between each Integer. This set of numbers includes all the numbers you can think of. It is called the set of Real numbers. Zero is in the middle of the number line so it is can't be the smallest number. Just like with the set of Integers the smallest Real number is negative infinity and the largest Integer is infinity.
Does that include every single number? No, there are still UnReal numbers. What is 100/0, or 10/0, or 1/0? You can't divide a number by zero and come up with anything that makes sense. There isn't a REAL number value for anything divided by zero. So any number divided by zero is an UNREAL number. The UnReal numbers aren’t on the Number Line they are off in space somewhere.

What makes a number odd or even? Simple, if you can divide it evenly by 2. In another words any integer that you can divide by two that creates another integer is even. 6/2=3 so 6 is an even number. 8/2=4 so 8 is an even number. 3/2=1 1/2 that is a Real number, but it isn't an Integer, it is somewhere between 1 and 2, so that means 3 is an odd number.

Every Integer can be divided by itself and one. A Prime number is a number that can ONLY be divided by itself and one. 8 can be divided by 1 & 8, it can also be divided by 2 & 4 so it isn’t a Prime Number. 7 can only be divided by 1 & 7 which makes it a Prime Number. Since any even number can be divided by two & another item that means that no Prime Number can be an even number.

There is one more thing about Real numbers. Real Numbers include Integers and fractions, but how many fractions do they include? Let’s look at ½, I can divide that by 2 and get ¼, I can divide that 2 and get 1/8, I can divide that by 2 and get 1/16. I can keep on doing this forever so I can’t list all the fractions between each Integer. That’s why I showed them as __ . There are an infinite number of fractions between each Integer. So the set of Real Numbers has an infinity of infinity numbers, but infinity + infinity or Infinity X infinity still equals infinity. Infinity isn’t a number it is a concept.

Integers include all the numbers that aren’t fractions and they run on forever in both directions.
Even numbers are Integers that you can divide by two and get another Integer.
Real Numbers are all those numbers you can think of.
UnReal Numbers are all the other numbers that don’t have a value you can understand. (What is 10/0 + 1/0? Well it would equal 11/0 but that is an impossible or an UnReal Number. 1/0 + 1 = 1 1/0 which is still an impossible or UnReal number. Therefore any UnReal number included in an equation makes the answer an UnReal number.)

Answer 2

Integers would be any number with only zeroes after the decimal point. It would include all the counting numbers (positive integers), their additive inverses (the negative integers), and 0. There is no smallest nor largest integer. You can think of negative and positive infinity as being smallest and largest but those aren't numbers, only concepts. An integer is odd if the last digit before the decimal point is 1, 3, 5, 7, or 9, even otherwise.

Answer 3

Wikipedia says the following:
"The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. A formal way of stating this: the integers are the only integral domain whose positive elements are well-ordered, and which has order preserved under addition. Like the natural numbers, the integers form a countably infinite set. The set of all integers is usually denoted in mathematics by a boldface Z (or blackboard bold, ), which stands for Zahlen (German for "numbers")"
There is not someting like the smallest or the largest integer because integers form a countably infinite set, as said before.
What determines if an integer is odd or even is the divisibility by 2. Even integers are divisible by 2 and odd numbers not.

Answer 4

Integer numbers are the set of the natural numbers with the set of their simetrics, like, {...,-4,-3,-2,-1,0,1,2,3,4,5,...}

There is no smallest integer, nor largest integer. An integer k is odd, if k mod 2 is 1, and even if k mod 2 is 0.

Answer 5

Integer Numbers : positive and negative numbers that do
have decimals e.g. ... ,-3,-2,-1, 0, 1,2,3,...

Smallest: infinity
Largest: infinity

if a integer is divided by 2 and there is a remainder then the integer is odd, otherwise its even. the negative signs play no role.

Answer 6

Ha ha, that turned right into a quite type of a shaggy dog tale, or i must assert a concepts boggling shaggy dog tale. that's quite simple chum. shall we initiate with a million, 2, 3,....., one hundred. all of us recognize that the sum of those numbers is 5050. Now keep including the subsequent numbers. you'll discover that the sum continuously will advance. Now enable a aspect come the position you ought to function infinity (i recognize that infinity is imaginary huge variety, yet I meant to assert that we ought to function greatest huge variety that your concepts can imagine). after we upload that, we come to entice close that the sum is terrifically higher, and wager what, that's tending to infinity. So kick that professor and discover some different person. you've also tried to discover that the progression approach. all of us recognize that the sum of the first n organic numbers is: n*(n-a million)/2 attempt putting greatest huge variety conceivable to imagine by using your mind, and back wager what, the sum has a tendency to infinity.

Answer 7

no