Original post by J4mi3Mike
prove that there is an infinite number of square numbers
What have you tried? If its by contradiction, what can you assume?
[Practically the solution]
If you wish to use proof by contradiction, your first line is always...
Next time, do at least write the first line down. It's standard enough that you should be able to do it.
What does this mean though? Can you rephrase it mathematically? In particular notice that...
Now, I wouldn't prove it by contradiction, but it requires a bit of machinery that's outside A Level Maths (though easy enough to have an inkling of what's going on).
A common trick in mathematics when we want to count things is to form a one-to-one correspondence with some other familiar stuff that we know how many there are. For instance...
In fact, this idea of "counting by forming one-to-one correspondence" leads to some weird consequences. I'll leave it as a cliffhanger.
If you wish to use proof by contradiction, your first line is always...
Spoiler
Next time, do at least write the first line down. It's standard enough that you should be able to do it.
What does this mean though? Can you rephrase it mathematically? In particular notice that...
Spoiler
Now, I wouldn't prove it by contradiction, but it requires a bit of machinery that's outside A Level Maths (though easy enough to have an inkling of what's going on).
A common trick in mathematics when we want to count things is to form a one-to-one correspondence with some other familiar stuff that we know how many there are. For instance...
Spoiler
In fact, this idea of "counting by forming one-to-one correspondence" leads to some weird consequences. I'll leave it as a cliffhanger.
(edited 7 months ago)
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