My favourite math fact is that 0.9999999.. is equal to 1. Exactly. Not approximately. Not as a rounded number. 0.9999 (recurring) is exactly 1.

Question. How the fuck does that work?

I tried explaining it here:

Here’s another perspective on why .999… repeating is exactly equal to 1.

For any two distinct real numbers, we can always find a rational number strictly between them, i.e. that rational number must be able to be expressed as a terminating decimal or a repeating decimal.  To be clear, that rational number is strictly between the two values; it is not allowed to be equal to either.

Suppose k is a rational number strictly between 1 and 0.9999….  If this is possible, then, I can write k exactly as either a decimal with finite digits, or I can write k as a repeating decimal.  The problem is, there are no decimals with finite digits between 1 and 0.999… , and there is no way to write a repeating decimal that is greater than 0.999… and still less than 1.  Either way, a k strictly between 1 and 0.999… does not exist.  The only way this can be true is if those two numbers are not actually distinct.  That is to say, 1 = 0.999…..

i truly appreciate how math seems like it’s this infallible always-true only-one-answer thing, when in reality math is just like:

I think the way to think abt it thats always made the most sense to me is

if x= 0.999999.....

10x= 9.99999.....

10x-x= 9

9x=9

x=1

so 0.9999....=1

I think next thursday is gonna be the best day of my entire life tbh

reblog for next thursday to be the best day of your life

not risking it

People who rely on “oof” “worm” “mood” “same” when faced with their friend’s emotional pain need to stop digging their heels in with “well its actual a complex way to say you relate and are here for them blah blah shit noises” reasoning and learn how to be emotionally available and supportive. No one wants to hear that all the time when they are going through it. If you don’t know what to say, just validate their emotions and care to write more than a single meme word.

And what are the Comfort Words you suggest?

Any variants of these are good, I use them a lot too. You know your friend best and you know yourself you gotta be realistic with how much you can help and what you can handle. Just talk with them to talk about boundaries. I know it can be awkward especially if the friendship is online but I’ve told my friends “hey I really can’t handle that atm but we can talk about x later” and I’ve also been told that what I’m saying was too intense and that she hears me and we can come and talk about it at a later date.

These things aren’t even dependent on feeling empathy because I know that’s a real struggle but just communicating your needs and boundaries and being honest about what you can and can’t handle and when is important to making healthy relationships. You don’t have to be people’s therapists(especially because that can be a recipe for diseater) but just listening and giving them space to be open with you is key. Respect their feelings and handle it how you would want someone to handle yours when you need it.

Typo fixed but it’s not even about saying the right chain of words but just being there for the people you care about and genuinely engaging with their pain instead of saying a meme phrase that does nothing

Before January ends, I’m going to magically and extremely be blessed by the universe.

not gonna risk scrolling past this

aw shit which january?

fuck your depression here’s what we’re doing

Don’t worry if your goals seem too far away or unreachable — if people tell you it’s never going to happen. People are wrong. The only person who can set limits in regards to what you can or should become is you. You’ll grow, one step after another, and soon enough you will look back and realize that you’ve become the person you’ve wanted to be, the person they didn’t believe could exist.

Psychology Daily - Quotes

Psychology Daily - Quotes

Effective Study Tips

1. Start early. Don’t leave studying to the last minute as cramming doesn’t really work. Preparing well in advance leaves you with time to ask questions and review topics you don’t fully understand.

2. Plan and organise your study time. Decide what you will do, in what order, and by what date.

3. Have an area that you designate specifically for studying. Don’t do anything else there. Keep all your notes, textbooks, materials etc in that area.

4. Study something each day – but allow yourself one whole day off a week. That way, you stay on top of your work without feeling bogged down and overwhelmed.

5. Make your own notes; rewrite material you’ve studied using your own words. Doing that, will help to consolidate your learning.

6. Cover up material you’re studying and try to summarise it, or to paraphrase it.

7. Don’t review material you know already. Assign your time to work that you still find challenging.

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Credit: Maya Beano