I cannot understand how there are “larger infinities than others” no matter how hard I try.

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I have watched many videos on YouTube about it from people like vsauce, veratasium and others and even my math tutor a few years ago but still don’t understand.

Infinity is just infinity it doesn’t end so how can there be larger than that.

It’s like saying there are 4s greater than 4 which I don’t know what that means. If they both equal and are four how is one four larger.

In: Mathematics

34 Answers

Anonymous 0 Comments

The main idea behind bigger infinity is that, with such big quantities, we rely on comparison and not actual “counting”.
If I can show that no matter what I do for every element of X there are 10 of y, y is definitely larger, right?

Now, go to Geogebra and plot the function y = X and y = x^2. Remembering that if a function “is over” the other then it’s bigger, x^2 is basically always over y=x and the more you go towards right and more the difference become larger. How larger? We can know it with a ratio!
Lim X -> infinity of X^2 / X = X and indeed, at infinity y=x^2 is infinitely larger that y=x.

This is not exactly what we means with bigger infinity but I hope I made sense in what comparing infinities means.

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