Mathematics and logic


(Disclaimer: I have ADHD and am completely useless when it comes to math. So please forgive me for being super-stupid on the subject.)

To my understanding, Mathematics are seen as completely logical. Which I don’t have a problem with except for when it comes to one certain thing in math that I just can’t make sense of as being considered logical:

Rounding of decimals.

To my understanding, the rule is that when you have a decimal that is 5 or higher, you round up. If 4 or lower you round down.

Two things that I don’t understand about this:

1. When you round up, you magically pull value out of the air that wasn’t there to begin with, and do the opposite when rounding down. How is this considered logical?

2. The rule isn’t applied universally. I’ve seen cases when, for example, making store purchases, no matter how low the decimal, it is rounded up and not down.

I appreciate any help you guys can give. Thank you in advance for the assistance! <3

In: 6

Rounding sacrifices precision for convenience. Essentially, there are plenty of situations where you don’t want to have a long string of numbers after the decimal point so you just pick a point to cut it off. We use the .5 as a rule of thumb in most cases just so everyone is on the same page, but in some cases it makes sense to always round up or down.
For example, when I’m doing carpentry, maybe I’ll need a piece of wood that’s between two of the marks on my tape measure. In that case I’ll round up for two reasons. I don’t have the equipment to make a precise enough measurement so I have to round. And I’m always going to round up because it’s easy to shave off a little more later if I need to.
Rounding is all about making numbers easier to use. So the logic comes in to determine how to best round a number to fit the situation.

I love your view of it 😀

You don’t magically add value… You approximate.. we do that when for the sake of simplicity we can lose precision

It’s like saying “bus arrives in hour” instead of “bus arrives in 58 minutes and 47 seconds” …

It is not logical…. It’s just simplified

And when it comes to stores… That’s not logical math, that’s economic and capitalism…. They round it up not because it is correct, but because they make more

Rounding numbers is a practical thing, so technically you are allowed to do it however you wish. What you’ve described is one convention, written down in textbooks. What the stores do is another convention that’s probably written down somewhere in their policies. There’s also something called “banker’s rounding” which rounds halfs to the nearest even number, so 5.5 becomes 6 and 8.5 becomes 8. In short, there are a lot of various rounding methods used for different purposes.

I don’t think anyone’s quite addressed the question yet. There’s a couple of things going on.

First, rounding is *convention*. It doesn’t make sense to talk about it being “logical” or “not logical”. It’s something we collectively agree to do in certain situations, not something you can prove.

For instance, I can prove, beyond a shadow of doubt, that there are infinitely many prime numbers or that it’s impossible to construct a regular heptagon with a straightedge and compass. These are mathematical *theorems*. I can’t, on the other hand, “prove” that 0.63 rounded should be 1 instead of 0.6, because we haven’t given rounding clearly defined rules. This is by design: We use it in whichever way is most convenient at the time.

Note that if I instead talk about “rounding to the nearest tenth”, then *that’s* a rigorously defined operation and I can start making factual statements about it. I can say that rounding 0.63 to the nearest tenth is 0.6, not 0.7 or 1.

I can also say that “rounding 0.63 gives 0.6”, and ask you to infer from that statement that I *meant* “rounding to the nearest tenth”. If you then turn around and say “0.63 rounded is 1”, you’re not *wrong* for disagreeing with me, we’re just using ambiguous language in different ways.

Second, math is *abstract.* I encourage you to let go of the idea that numbers embody “value”, or that there was anything “there to begin with”. Rounding is just another operation that takes a number as an input and spits out another number as an output, no different from, say, adding 1, or squaring, or taking the cube root.

Thank you everyone! I get it now! You’re all awesome! <3