Why do you need to know arithmetic when you can use a calculator?

>>8850597
You don't really need it because sure, you could use a calculator to help you out, but arithmetic is like a training grounds for abstract symbol manipulation. Arithmetic is the fisher price symbol manipulation kit. The manipulations are simple and they are also easy to check for correctness.

Another reason would be because a calculator can't tell you the answer for this:

Find the last 2 digits of the number 3^2013

Very few people would be able to handle the abstractness of mathematics without even being able to perform arithmetic.

>>8850597
It's good for your brain.

>>8850639
this, basically. You could theoretically plug in any integral into wolfram, but it woudlnt help you understand what a force integral means

>>8850615
(3^2013) % 100

>>8850597
Why do you need vocabulary when you have a dictionary?

>>8850597

So that you understand what the calculator is doing.

>>8850597
Why learn physics when you can just ask a physicist?

>>8850768
>(3^2013) % 100
Well, solving that is a way to find that but as you have given it to me, it is wrong. I asked for 2 digits and you gave me an equivalence class of integers.

Someone failed number theory I see.

>>8850783
>He doesn't know how to evaluate it in a calculator

Fucking moron.

>>8850804
The number is too big for a calculator.

>>8850836
>His calculator doesn't support large numbers with arbitrary precision

Okay, kiddo.

Memes aside, if you want to do a maths degree you need to be good at arithmetic. Differentiating a function, expanding brackets, mulitiplying matrices etc.

>>8850783
% represents remainder after division. Remainders are not equivalence classes.

Seriously how autistic can you get. I'm guessing your intro number theory final is coming up next week?

>>8850615
>Another reason would be because a calculator can't tell you the answer for this:

>Find the last 2 digits of the number 3^2013

A calculator can't do it but you can do it in your head?

>>8850905
I can factor 2013 = 100*20 + 13 in my head

I can calculate 3^20 mod 100 in my head
I can calculate 3^13 mod 100 in my head

And that's all I need.

>>8850937
Calculators can do that too.

>>8850597
Knowing arithmetic allows for basic principles of knowledge to be obtained. How would you use a calculator without knowing what to punch in and the order in which to do so?

>>8850955
Yeah, but a calculator will not give you the answer.

You can use it to find relevant facts about the multiplicative cyclip group generated by 3 modulo 100 but a calculator won't do that automatically like it would do if you asked it what is 3^50 for example.

>>8850597
If you had to pull out a calculator anytime you had to do simple arithmetic.. fuck. I can do it in my head faster than on a calculator. A calculator is only useful because the human mind stops being good at for double digit numbers.

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>>8850615
Actually it's 23

>>8851007
Damn that's a powerful calculator. My HP 10s+ Scientific Calculator can't calculate that high. After 3^209 it breaks.

But actually the question is the same if I ask you what are the last two digits of 3^20000000000000000000013

And you cannot plug that into a calculator. But just so that the answer is different. What are the last two digits of
3^20000000000000000000000000014

>>8850597
Why know how to eat when you can just use an iv? Why write when you can just use a webcam? Why live when you can just kill yourself???

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>>8851021
some good questions there

>>8850597
To know what your doing, and why your doing it.
But then again using a calculator for 0/4 or 4+7 is its own punishment

>>8850597
why do you need to eat food if it can be fed to you in a tube?

>>8851012
2^200...014 is the same as 2^2014 so they are 23*3 = 69
But seriously I agree with you, a calculator is just a tool

>>8851114
A calculator won't tell you 3^20...14 is the same as 3^2014. But glad you agree.

>>8850773
this

>>8851137
Well don't wanna be annoying but 3^100 ends with ..001 so since 3^20...0014 is (3^2014)*×(3^100)×...×(3^100), it is the same as 3^2014
You can check that 3^113, 3^213 and 3^2013, and any other 3^(113+k*100) end all with 23

>>8850597
To know if you fucked up PEMDAS when entering it in your calculator

>>8850597

Because it's easier to do arithmetic with some fractions then plug a complicated result into my calculator then get a bunch of rounding errors.

Calculators are inexact, fractions are beautiful and simple.

>>8850597
How many decimals of pi and sqrt 2 are you willing to write out?
>whatever your answer is it's not enough