For the last time, I ask you to substitute the a,b,c,d in "(a+b·d)·c mod b = a·c mod b" with appropriate values to get "((−1)+3·3)·8 mod 3 = ...". Fill it in.
Honestly, you still don't understand mathematical rigour, and you're not going to benefit if you keep insisting on doing things your way. Instead of writing things your way 7 times, just follow my instructions carefully once, then we can move on. I can teach, but I cannot force anyone to learn.
For the last time, I ask you to substitute the a,b,c,d in "(a+b·d)·c mod b = a·c mod b" with appropriate values to get "((−1)+3·3)·8 mod 3 = ...". Fill it in.
I already wrote the left side of the statement I told you to complete. If yours does not match mine, it is automatically wrong.
It is hard for me to know what really is going on in your head. If I tell you what "(−1)·8" means, you will just say "I know", and I have no clue whether you really know.
The expression $ m^n $ is called a power and described in words as $ m $ to the power $ n $. The number $ m $ is the base of the power, and the number $ n $ is its exponent .
So we can interrupt same for - 1^8=and any natural number $ n $, $\displaystyle m^n = \underbrace{m\times m\times \ldots \times m}_{\hbox{\( 8 \)~factors~\( m \)}} $
"interrupt" ≠ "interpret". And I think we really need to go back to the basics, because you're not reading basic expressions in the correct way at all. First, a basic arithmetic expression is made of symbols, including basic operations addition, subtraction, multiplication, division, negation, numbers, and brackets.
@yuvrajsingh: Tell me the difference between subtraction and negation.
And for us to write down an arithmetic expression, there must be rules so that it is unambiguous. The first rule is that we must be able to match brackets.
So listen to me carefully. I am describing the rules for writing arithmetic expressions. As I said above, you must have matching brackets and to evaluate an expression you must evaluate what is within matching brackets first before anything outside.
In the above messages yesterday, you kept writing expressions like "−(1)^8". Based on what I just said, this makes no sense, because it is evaluated exactly the same as "−1^8", since there is just a single number within the matching brackets.
So there is some incorrect reason that you are putting brackets in that manner. And that same reason is why you kept getting the wrong answer for previous questions. Don't need to explain that. I will continue describing the rules then you will know.
I will follow, the way but you won, t stop this in between I mean one you come say now it is over, and next you have to teach me algebra, trigno, calculus, coordinate geometry, they way you want, and time u want, I will follow each and every command, before asking anything, so do you ready to give me this promise? @user21820
Rule 1: It must have matching brackets and to evaluate it you must evaluate what is within matching brackets first before anything outside. Rule 2: Certain operations have precedence over others. Some have the same precedence. For operations of the same precedence, we specify whether we perform them from left to right or from right to left. I will give the precedence table below.
In each row I list the operations of the same precedence between {}, and specify ltr (left-to-right) or rtl (right-to-left). The higher row has higher precedence.
{^} : always put brackets (because people do not all agree on whether it should be ltr or rtl).
{·,/} : ltr
{negation} : rtl
{+,subtraction} : ltr
For example, according to the above rules, "−1+2" is evaluated the same as "(−1)+2", because negation has higher precedence than +.
In each row I list the operations of the same precedence between {}, and specify ltr (left-to-right) or rtl (right-to-left). The higher row has higher precedence.
Higher precedence means it is done first...
Now look at where "^" and "−" appear in the table...
No, I want you to put brackets to force the evaluation to be correct without precedence rules...
The precedence rules are there only to reduce the number of brackets we have to write. But you must be able to use brackets in place of the precedence rules.
In the above messages yesterday, you kept writing expressions like "−(1)^8". Based on what I just said, this makes no sense, because it is evaluated exactly the same as "−1^8", since there is just a single number within the matching brackets.
I'm sorry to say but I think you have a severe problem understanding basic English. I never seem to be able to get you to follow my instructions no matter how clear I make them.
No you didn't. I said "I asked you to express THAT using exponentiation".
I never asked you to simplify or calculate anything.
If you have difficult understanding basic English like "express ... using ...", you may have to improve your English otherwise it is very time-consuming for me to teach anything to you.
@yuvrajsingh Sadly, I can't even understand what you're saying except "give me a last chance". Sure, but you really need to work on your English.
"9^4" is how you can express "9·9·9·9" using exponentiation.
If you understood exponentiation, I really see no reason you cannot express the other side of "9.9.9.9 mod 10 = (-1).(-1).(-1).(-1) mod 10." using exponentiation as well.
Go ahead and try to answer my question again, but you really need to put in a lot of effort into improving your English, especially if you want to do mathematics, because English is the current language used by most mathematicians.
Is that you do not understand basic English. I have no choice but to give up; I can't afford to spend so much time on just you.
Let me just give you the answer and that's it.
I asked you to express:
> 9.9.9.9 mod 10 = (-1).(-1).(-1).(-1) mod 10.
using exponentiation.
The correct answer is:
> 9^4 mod 10 = (−1)^4 mod 10.
Such a simple goal, but you could not understand. How can I teach you like this? Normally I like to let people figure out everything themselves with suitable hints, but you don't even understand the English in my hints...
It's not that I quit. It's that I think I cannot teach you as well as other people because you do not understand enough English to follow my instructions.
If you want my advice, you can wait a few days, but if the pain comes back or there is swelling you should go to a doctor/dentist, because it is not normal and may need urgent treatment. If it goes away in the next few days, then I suppose you can ignore it.
