11. Can there be more than one infinity?

Simple answer: yes.

This video basically describes how:

I’ve been diving a bit into infinity with this online class. Part of trying to understand this is realizing that I’ve held certain concepts in my head there were wrong.

I had this idea that infinity is the biggest you can get to. But that’s not really what infinity is. If I have an infinite amount of natural number (1,2,3,4,5 . . . ), I still have constraints of what that infinity means. There is an infinite amount of natural numbers, yes. But I’m still just dealing with natural numbers.

There are also an infinite amount of rational numbers (think fractions/decimals) between 0 and 1.

Some infinities are bigger than other infinities. You can compare infinities by doing a bijection of one set to another. If you can connect each entry in one set to a corresponding entry in another set and vice versa, then the sets are the same size. To prove whether infinities are the same or different size, you just have to create a rule or process to form a bijection.

If I have infinite rational numbers, then this is bigger than infinite natural numbers. I can count infinite natural numbers. But infinities do not have to be countable.

There is a diagonal proof that basically says this: try to write a list of all the rational numbers in decimal form. Now take the first digit of the first number and change that digit. Then take the second digit of the second number and change that. The third number, change the third digit. And if you keep changing the digits on for infinity, then the number you end up with will not be on your list. Thus, the rational numbers are not countable and are bigger than the set of natural numbers.

There are also an infinite amount of infinities that are larger and larger than another.

I had a concept of infinity that was incorrect. But it was useful to me, until I wanted to learn more and I had to change what I thought.

Mistakes

I’m not very good at making mistakes. I hate making mistakes, which means I find myself falling into a pit of despair. Sometimes I become unable to function as I think that I’ve irrevocably fallen off my (completely imaginary) pedestal of perfection.

Here’s the truth: everyone¬†makes mistakes on a daily basis. It’s part of life. We are all very far away from perfection and we all do horrible things.

But still, one small mistake can ruin my day. I fall into my abyss of guilt because I want to go back and change what happened (which is impossible). I feel deep discouragement because I think there is no way to fix it.

And sometimes we make mistakes that we can’t really fix. We might hurt someone’s feeling so badly that it changes our relationship forever. We might wreck our car. We might wreck part of our life.

We can’t change the past. Mistakes happen, and the consequences can last a very long time. That hurts.

But I’ve been learning how to avoid the pit of despair and move forward. Here are ways to deal with mistakes better:

1. Accept what happened.

Not too long ago, I learned about “radical acceptance.” This means accepting life how it is, totally and completely. It means we accept that things happened and we can’t change them. Acceptance can be very difficult. We might think life is unfair. We might want something different.

But reality is what it is–and it’s a lot easier to accept it (possible) than to fight against it (impossible). It can take practice and patience, but we can accept that we made mistakes and we can’t change what we did.

2. Fix what you can.

Instead of dwelling on what we did, we can take some time to think about what we can do to make right. When I yell at my children, I can’t take back that yelling. But I can apologize. I can start speaking kindly to them. I can give them hugs and cuddles. I can work harder to not yell as much in the future.

Fixing things doesn’t always make the mistake go away completely–there are often scars. But people can forgive–and we can forgive ourselves, knowing that we’re trying.

3. Laugh at yourself.

Often, many mistakes we make are small and unimportant. And they can be hilarious, if we have the right perspective. We may slip and fall, but we can also laugh at how silly it all was. We can laugh at botched recipes, bad haircuts, forgotten information, fumbled words, and awkward encounters. We can laugh when our mistakes don’t define us, when we realize everyone makes mistakes, and that we don’t have to be perfect (or even close to it).

4. Learn from mistakes.

If we do something wrong, we don’t have to keep doing it over and over again. We can learn. We can know that we can do better. We can change. That offers a lot of hope to keep at it and to keep climbing towards being a better version of ourselves.

5. Repent.

The Atonement of Jesus Christ makes it so that we can be completely forgiven and change for the better. It means that even those scars can be healed and there is almost nothing we can do to completely ruin our lives. We can be saved from our mistakes, not matter how small or how big. There is always hope.