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What Does the Upside-Down A Mean in Math?

We typically associate Latin script letters (A, B, C, etc.) with the English language. These letters are easy to understand, unlike pesky mathematical Σ’s and π’s. However, letters can have very familiar forms in various disciplines, such as the upside-down A in math (∀). The ∀ symbol may look like the familiar capital “A” written …

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Appreciation of or for: When to Use Each Preposition in Conjunction with Appreciation

We’ve all greatly appreciated a friend’s help or an act of kindness from a stranger, but when it comes to recognizing a person’s thoughtfulness, which is correct: “appreciation of” or “appreciation for”?  The correct way to communicate appreciation depends on the context. If you are showing that you appreciate someone for the benefits or qualities …

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Real Time or Real-Time: When to Use a Hyphen (And When to Skip It)

You’ll find that quite a few things happen in real-time — or is it “real time”? To hyphen or not to hyphen: that is the question. If you find that you’re uncertain, you aren’t alone. The correct way to spell “real time,” with or without a hyphen, depends on your intended meaning and syntax. If …

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Knowledge on or Knowledge of: Which Is Correct?

Choosing the right preposition to follow a noun can be tricky for English as a second language. Even native speakers often find it hard to know and explain why they choose a particular preposition which “sounds” better than another. For instance, is it “knowledge on” or “knowledge of”? “Knowledge of” is the preferred prepositional phrase …

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High Quality or High-Quality: Understanding When to Use a Hyphen

Some would say hyphens are going the way of dinosaurs, disappearing in favor of compound words. But they are not extinct just yet, so knowing when to use one and when to skip it is important.     The difference between “high-quality” and “high quality” is determined by the location of the noun that the phrase should …

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