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Couples often debate whether children should be invited to a wedding. Luckily the answer is simple- it's up to you! Children can be great fun at weddings as they often add to the merriment. But it's certainly not rude to only invite adults. Some couples choose to only invite children over a certain age (say 10 years old, etc.) as a compromise. It's always a little tricky to relate this to your guests, but it can be done tastefully.
The best way to invite your guests to include only the guests names on the invitations...simple, right? This can often be done by writing your guests full name (Mr. and Mrs. John Temple) and the address on an Outer Envelopes and then specifically listing guests by first name (John and Abagail) on the inner envelope. This makes it extremely clear who is invited, when little Timmy isn't listed. This is the proper protocol when not inviting children, or when asking your guests to not bring a date.
You may find that some of your guests "overlook" your proper etiquette and will Rsvp that their children will be attending with them. This is a great time to call your guests and explaining why you are not inviting any children (budget, location, formality, etc.). Gently but firmly stand by your choice- I promise you someone will try to talk you out of it no matter how you decide!