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1. My score is three times higher than your score.
2. My score is three times as high as your score.
Is there any difference in meaning between the two sentences ?
The way I see it ,"My score is three times as high as your score" means that if your score is 1 my score is 3.
But I have some doubts regarding the first sentence,"My score is three times higher than your score".
This sentence can either mean the same as the second sentence or it can mean that if your score is 1 my score would be three times i.e. 1*3=3 higher than your score i.e. 4.
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Comments  
What you say is technically correct, but I'm afraid you'd only get sympathy from a mathematician.
Unfortunately, people generally understand #1 to mean the same as #2.
Your two sentences have the same meaning. The word times can refer only to multiplication, not addition. I'm afraid not even a mathematician would agree with you.
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Hi, Ivan,

So what would "One time higher" mean? Are you claiming it would not be higher at all??

Best regards, - A.
AvangiHi, Ivan,

So what would "One time higher" mean? Are you claiming it would not be higher at all??

Best regards, - A.

Yes, exactly.

AvangiOne time higher
I've never heard this expression. Is it really used?

three times as high as = three times higher than

in my book.

CJ
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I'm just saying that "higher" means "higher."
"Three times higher" is a dumb, useless expression, a non-sequitur.

This is as high as that.
This is higher than that.

These do not mean the same thing at all! Emotion: shake
Avangi"Three times higher" is a dumb, useless expression, a non-sequitur.
Yes, I suppose it is. I just take it to mean This is higher than that by a factor of three.

CJ
CalifJim This is higher than that by a factor of three.
Thanks. I believe I understand "where you're coming from." But I'm still struggling.
You could say, "Let's raise this by a factor of three." Fine. You're describing a process: multiplication.

But to me, the expression "This is higher than that BY X" describes addition, even if X includes another process.
This is higher than that by a factor of zero. Common sense says there's no change.

But I think you and Dim would say it's now calculated out of existence. [:^)]
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