The pattern
X modulo Y
is an informal but common parlance in technical, especially mathematically, oriented talk. It is used to mean informally 'X, ignoring Y'. For example,
"The rocket design was flawless, modulo the toxic waste produced by its fuel."
The meaning is inspired by, but not perfectly corresponding to, the arithmetic modulo function (for example, clock-time addition) which when suitably abstracted involves 'collapsing' all items of a set into the special items of the set, so that the full set does not need to be dealt with (this is where the associated meaning of 'ignoring' comes from).
In your interpretation "note what parts of it still need to be modified", the 'modified' part is irrelevant. 'Modulo' is pragmatically "I'm telling you about the most important part (the X), but remarking on the existence of some part that might be important for other reasons but under the current context we want to ignore (the Y)".
I only see this usage from academics with a background that includes England. It is used to mean the opposite of except - some part of the set is included, not excluded, and you're saying that you're including it even though some people might not. It isn't a substitute for but or except, because those would be about excluding something from the set. It might be closer to even though.
In math, modulo is the remainder after dividing, so 5 mod 2 is 1. In words, it's something like even after accounting for. However, it has been heard by generations of people who aren't sure what it means, don't want to ask, and feel that smart people use it. Those people tend to use it as except or but, meaning that you probably can't be entirely sure any more what someone means when they use it.
Videos
(This explanation is only for positive numbers since it depends on the language otherwise)
Definition
The modulo operation returns the remainder or signed remainder of a division, after one number is divided by another, the latter being called the modulus of the operation. (source: wikipedia)
For instance, 9 divided by 4 equals 2 but it remains 1. Here, 9 / 4 = 2 and 9 % 4 = 1.
Image source: Wikimedia
In your example: 5 divided by 7 gives 0 but it remains 5 (5 % 7 == 5).
Calculation
The modulo operation can be calculated using this equation:
a % b = a - floor(a / b) * b
floor(a / b)represents the number of times you can divideabybfloor(a / b) * bis the amount that was successfully shared entirely- The total (
a) minus what was shared equals the remainder of the division
Applied to the last example, this gives:
5 % 7 = 5 - floor(5 / 7) * 7 = 5
Modular Arithmetic
That said, your intuition was that it could be -2 and not 5. Actually, in modular arithmetic, -2 = 5 (mod 7) because it exists k in Z such that 7k - 2 = 5.
You may not have learned modular arithmetic, but you have probably used angles and know that -90° is the same as 270° because it is modulo 360. It's similar, it wraps! So take a circle, and say that its perimeter is 7. Then you read where is 5. And if you try with 10, it should be at 3 because 10 % 7 is 3.
Two Steps Solution.
Some of the answers here are complicated for me to understand. I will try to add one more answer in an attempt to simplify the way how to look at this.
Short Answer:
Example 1:
7 % 5 = 2Each person should get one pizza slice.
Divide 7 slices on 5 people and every one of the 5 people will get one pizza slice and we will end up with 2 slices (remaining). 7 % 5 equals 2 is because 7 is larger than 5.
Example 2:
5 % 7 = 5Each person should get one pizza slice
It gives 5 because 5 is less than 7. So by definition, you cannot divide whole 5items on 7 people. So the division doesn't take place at all and you end up with the same amount you started with which is 5.
Programmatic Answer:
The process is basically to ask two questions:
Example A: (7 % 5)
(Q.1) What number to multiply 5 in order to get 7?
Two Conditions: Multiplier starts from `0`. Output result should not exceed `7`.
Let's try:
Multiplier is zero 0 so, 0 x 5 = 0
Still, we are short so we add one (+1) to multiplier.
1 so, 1 x 5 = 5
We did not get 7 yet, so we add one (+1).
2 so, 2 x 5 = 10
Now we exceeded 7. So 2 is not the correct multiplier.
Let's go back one step (where we used 1) and hold in mind the result which is5. Number 5 is the key here.
(Q.2) How much do we need to add to the 5 (the number we just got from step 1) to get 7?
We deduct the two numbers: 7-5 = 2.
So the answer for: 7 % 5 is 2;
Example B: (5 % 7)
1- What number we use to multiply 7 in order to get 5?
Two Conditions: Multiplier starts from `0`. Output result and should not exceed `5`.
Let's try:
0 so, 0 x 7 = 0
We did not get 5 yet, let's try a higher number.
1 so, 1 x 7 = 7
Oh no, we exceeded 5, let's get back to the previous step where we used 0 and got the result 0.
2- How much we need to add to 0 (the number we just got from step 1) in order to reach the value of the number on the left 5?
It's clear that the number is 5. 5-0 = 5
5 % 7 = 5
Hope that helps.
Mathematics would say: "10 is congruent to 1 modulo 3". The modified usage "10 modulo 3" with "modulo" as an operation (like "10 plus 3") is from computer programming.
The verb in your sentence is equals. The entire sentence can be parsed either as 10 modulo 3 being a noun phrase with modulo 3 operating as an adjective, or as modulo 3 equals being a verb phrase with modulo 3 operating as an adverb. Whichever analysis is preferred, the usage is perfectly standard, if slightly imprecise. The reference you cite is correct to prefer is congruent to over equals.
I have a test tomorrow, in the test one of the questions will be to seperate a number from a 3 digit number, say I have 641, I need to know how to print out 6,4 and 1 seperately.
What the hell do I do ? The teacher is so bad I couldn't understand a word she said and neither did my class, we already complained about her but this isn't the issue, the issue is that I have no easy answers on the internet for what the modulo is.
Why does doing (n/100)%10; print out the hundred digit ? I have no idea how this works, please go easy on me.
