I
noun
BAD : The increase of crime is accelerating.
GOOD : The increase in crime is accelerating.
BAD : There has been an increase of the number of cars.
GOOD : There has been an increase in the number of cars.
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increase in sth (NOT of ): 'There's been a sudden increase in political activity.' 'We can expect further increases in the cost of living.'
II
verb
1
BAD : I'd like to increase my English.
GOOD : I'd like to improve my English.
BAD : We can increase the economic situation by working harder.
GOOD : We can improve the economic situation by working harder.
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increase = become or make (something) greater in amount, number or degree: 'The government has increased taxes.' 'As their profits increase, the companies expand.' 'The number of words in the language is increasing all the time.'
improve = become or make (something) better: 'Efforts are being made to improve the quality of the medical services.'
2
BAD : The government is trying to increase the level of education.
GOOD : The government is trying to raise the level of education.
BAD : In Hong Kong the standard of living has increased sharply.
GOOD : In Hong Kong the standard of living has risen sharply.
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When you are talking about the level or standard of something, use raise/rise (NOT increase ): 'The standard of living continues to rise.'