## Even bigger than infinity?

We can look at Hilbert’s hotel and other such problems, but to really understand the extent to which infinities reach, we need to know about a way of thinking called Set Theory.

A set is simply a collection of any objects or symbols, usually written inside curly brackets {} and separated by commas. For example, the set A might be written as “A = {1, 3, 5, 7}”

. We call the size of the set the cardinality, which is just the number of elements within the set. For A, the cardinality is 4. When two sets have the same ‘cardinality’, we can pair them, which is called a ‘bijection‘.

If we now think about an infinite set, for example, B = {1, 3, 5, 7, 9, 11…} or simply the natural numbers; N = (1, 2, 3, 4, 5, 6…}. The cardinality of this set is…

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## Quest

“Everything you possess of skill, and wealth, and handicraft,
wasn’t it first merely a thought and a quest?”  ― Jalaluddin Rumi

“Say it, reader. Say the word ‘quest’ out loud. It is an extraordinary word, isn’t it? So small and yet so full of wonder, so full of hope.” ― Kate DiCamillo, The Tale of Despereaux

“Heroes know that things must happen when it is time for them to happen. A quest may not simply be abandoned; unicorns may go unrescued for a long time, but not forever; a happy ending cannot come in the middle of the story.”  ― Peter S. Beagle, The Last Unicorn

“You  didn’t get the quest you wanted, you got the one you could do.”  ― Lev Grossman, The Magician King

“Not all those who wander are lost.”  ― J.R.R. Tolkien, The Fellowship of the Ring

“It is the mission of each true knight…
His duty… nay, his privilege!
To dream the impossible dream,
To fight the unbeatable foe,
To bear with unbearable sorrow
To run where the brave dare not go;
To right the unrightable wrong.

To love, pure and chaste, from afar,
To try, when your arms are too weary,
To reach the unreachable star!

This is my Quest to follow that star,
No matter how hopeless, no matter how far,
To fight for the right
Without question or pause,
To be willing to march into hell
For a heavenly cause!

And I know, if I’ll only be true
To this glorious Quest,
That my heart will lie peaceful and calm
When I’m laid to my rest.

And the world will be better for this,
That one man, scorned and covered with scars,
Still strove, with his last ounce of courage,
To reach the unreachable stars!”
― Joe Darion, Man of La Mancha

In response to Daily Photo Challenge Quest